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Electrical Circuit and Circuit Analysis (BCA Part-I)
Ashish Sharma M.Sc. (Physics)
Anupama Upadhyay Revised By: Mr Vijay M.Sc. (Physics)
Lecturer Deptt. of Information Technology Biyani Girls College, Jaipur
2 Published by :
Think Tanks Biyani Group of Colleges
Concept & Copyright :
Biyani Shikshan Samiti Sector-3, Vidhyadhar Nagar, Jaipur-302 023 (Rajasthan) Ph : 0141-2338371, 2338591-95 Fax : 0141-2338007 E-mail :
[email protected] Website :www.gurukpo.com; www.biyanicolleges.org
ISBN: 978-93-81254-34-2
Edition : 2011 Price :
While every effort is taken to avoid errors or omissions in this Publication, any mistake or omission that may have crept in is not intentional. It may be taken note of that neither the publisher nor the author will be responsible for any damage or loss of any kind arising to anyone in any manner on account of such errors and omissions.
Leaser Type Setted by : Biyani College Printing Department
Electrical Circuit and Circuit Analysis
3
Preface
I
am glad to present this book, especially designed to serve the needs of the
students. The book has been written keeping in mind the general weakness in understanding the fundamental concepts of the topics. The book is self-explanatory and adopts the “Teach Yourself” style. It is based on question-answer pattern. The language of book is quite easy and understandable based on scientific approach. Any further improvement in the contents of the book by making corrections, omission and inclusion is keen to be achieved based on suggestions from the readers for which the author shall be obliged. I acknowledge special thanks to Mr. Rajeev Biyani, Chairman & Dr. Sanjay Biyani, Director (Acad.) Biyani Group of Colleges, who are the backbones and main concept provider and also have been constant source of motivation throughout this Endeavour. They played an active role in coordinating the various stages of this Endeavour and spearheaded the publishing work. I look forward to receiving valuable suggestions from professors of various educational institutions, other faculty members and students for improvement of the quality of the book. The reader may feel free to send in their comments and suggestions to the under mentioned address. Author
4
Syllabus B.C.A. Part-I
Electrical Circuit and Circuit Analysis [This course is of introductory nature, and therefore, emphasis will be on basic concepts and direct applications of mathematical expressions without rigorous analysis] Electric Charge, Conductors and Insulators, Coulomb‟s Law, Quantization and Conservation of Electric Charge, Electric Field, Electric Lines of Force and Gauss‟s Law of Electrostatics, Electric Potential Energy and Electric Power. Capacitors, Capacitance, Capacitors in Series and Parallel, Capacitors with Dielectric. Electric Current, Resistance, Resistivity and Conductivity, Ohm‟s Law, Electromotive Force, Series and Parallel Combination of Resistance, Current in a Single Loop, Electrical Power Consumption, Multiloop Circuits, Kirchhoff‟s Current Law, Kirchhoff‟s Voltage Law, Charging and Discharging of a Capacitor. Magnetic Field due to a Bar Magnet, Biot-Savat‟s Law, Magnetic Field due to a Current Carrying Coil, Force between Two Parallel Currents, Magnetic Field inside Solenoid and Toroid, Magnetic Flux, Faraday‟s Law of Electromagnetic Induction, Magnetic Properties of Material (diamagnetic, paramagnetic and ferromagnetic materials), Induction, Energy Stored in a Inductor, L-R Circuits. Generation of Alternating EMF, Average and RMS Value of AC, Analysis of AC. Circuits (Series L-R, Series R-C, Series LCR, Parallel LCR Circuit), Resonance, Three Phase AC Circuits. DC Generator, DC Motor, Transformer, Single Phase Induction Motor, Three Phase Induction Motor. Measuring Instruments, Multimeters. House Wiring Material and Accessories, Types of Wiring, Basic Principle of Earthing, Wiring Layout for a Computer Lab. Four Terminal Network Analysis, Network Theorems, Superposition, Thevenin, Norton, Reciprocity, Compensation and Maximum Power Transfer Theorems.
□□□
Electrical Circuit and Circuit Analysis
5
Content S. No. 1.
Name of Topic Electrostatics 1.1 Conductors 1.2 Insulators 1.3 Charge 1.4 Coulombs Law 1.5 Electric Field 1.6 Electric Flux 1.7 Potential 1.8 Potential Energy 1.9 Electric Power
2.
Capacitors 2.1 Capacity 2.2 Capacitor 2.3 Spherical Capacitor 2.4 Combination of Capacitors 2.5 Gang Condenser
3.
Current Electricity 3.1 Ohm‟s Law 3.2 Specific Resistance 3.3 EMF & Terminal Voltage 3.4 Combination of Resistances 3.5 Kirchhoff‟s Law 3.6 Charging and Discharging of Capacitors 3.7 Time Constant of RC Circuit
4.
Magnetism 4.1 Magnetic Induction 4.2 Biot-Savart‟s Law 4.3 Magnetic Flux
6
S. No.
Name of Topic 4.4 4.5 4.6 4.7 4.8
Lenz‟s Law Faraday‟s Laws of EM Induction Diamagnetic, paramagnetic and Ferromagnetic Materials Self Induction Mutual Induction
5.
Alternating Current 5.1 Current 5.2 AC Generator 5.3 Impedance & Reactance 5.4 AC Circuit containing L, C & R 5.5 Power in AC Circuit 5.6 Power Factor 5.7 Star and Delta Connection of Three Phase AC
6.
Electrical Devices, Machines and Measuring Instruments 6.1 DC Motor 6.2 Transformer 6.3 Ammeter 6.4 Voltmeter 6.5 Multi-meter
7.
Electric Wiring 7.1 Fuse 7.2 Earthing 7.3 Wiring
8.
Network Analysis 8.1 Thevenin‟s Theorem 8.2 Norton‟s Theorem 8.3 Maximum Power 8.4 Transfer Theorem
9.
Unsolved Papers 2011 to 2006
□□□
Electrical Circuit and Circuit Analysis
7
Chapter-1
Electrostatics Q.1
Differentiate between conductors and insulators on the basis of flow of charge?
Ans.: Conductors: Conductors are the materials through which electric charge flows easily. In general metals are good conductors. Examples – Silver, Copper etc. Insulators: The poorest of conductors in which the charge does not flow under normal conditions are called Insulators. In general nonmetals are insulators. Examples – Glass, Paper etc. Q.2
Explain different properties of Charge.
Ans.: Charges are of two types: (a)
Positive Charge
(b)
Negative Charge
Some properties of Charge:
Q.3
(i)
Two charged bodies attract each other or repel one another depending on the nature of charge present on them.
(ii)
Charge is a quantized quantity and the quantum of charge is equal to the electronic charge in magnitude.
(iii)
In every isolated system the total charge remains constant i.e. the algebraic sum of positive and negative charge does not change in any process taking place in the system.
Define Coulomb’s Law and explains Absolute Permittivity.
Ans.: Coulomb’s Law: According to this law “stationary charges repel or attract each other and the attractive or repulsive force is directly proportional to the
8
magnitude of charges and inversely proportional to the square of the distance between them.” F
q1q2
and
F
1 / r2
i.e.
F
q1q2 / r2
=>
F
=
K q1q2 / r2
K
=
Constant
K
=
9 X 109
where In M.K.S. System
Absolute Permittivity : Absolute Permittivity of the medium is equal to the multiplication of permittivity of free space (ε0) and relative permittivity (εr) i.e. ε0 εr . Permittivity shows the ability of the medium as to many electric lines of force can pass through that medium. Q.4
Define Electric Field and explain properties of Electric Lines of Forces with the help of diagram.
Ans.: Electric field: The region in which a stationary charged particle experiences a force (other than the gravitational force) is called electric field. An Electric Line of Force is that imaginary smooth curve drawn in an electric field along which a free and isolated unit positive charge will move. Properties of Electric Lines of Force : (i)
Electric lines of force are imaginary and start from a positive charge and end on a negative charge.
Electrical Circuit and Circuit Analysis
Q.5
9
(ii)
The tangent drawn at any point on the line of force gives the dir n of resultant electric field at that point.
(iii)
No two lines of force intersect each other.
(iv)
These lines have a tendency to contract along the length like a stretched elastic string. This explains attraction between opposite charges.
(v)
These lines have a tendency to move apart from each other in the dir n normal to their length. This explains the repulsion between like charges.
What do you mean by Electric Flux?
Ans.: Electric Flux: The number of electric lines of force passing through an area perpendicularly is called Electric Flux. Electric flux depends on the angle „θ‟ between area vector „da‟ and dir n of electric lines of force and is given by dФ = EdaCosθ There may be three conditions: (i)
When the frame is perpendicular to dirn of electric field, In this case angle θ between da & E is 0°. So electric flux
10
dФ = EdaCos0° or
dФMax = Eda
da
Ф = Eda
(ii)
E
da
E
If the frame is parallel to the dirn of electric lines of force then θ = 90° and flux dФ = EdaCos90° dФ = 0 will be zero i.e. minimum. (iii)
da
θ
E
For any other orientation, the electric flux will be dФ = EdaCosθ
E
Electrical Circuit and Circuit Analysis
Q.6
11
State Gauss’s Law of Electrostatics. What is its essence?
Ans.: Gauss’s Law of Electrostatics : According to this law, “The total electric flux of an electric field through a closed surface is equal to 4 k or (1 / ε0) times.” The net charge enclosed by that surface i.e.
Ф = 4пk∑q = 1 /ε0∑q
Where ∑q = q1 + q2 + q3 + . . . . . . . . . . (total no. of charges inside the surface) Essence of This Law : This law suggests that the flux through any closed surface is a measure of total charge inside it. For the field lines that originate on a positive charge must either pass out through the surface or else terminate on a negative charge inside. On the other hand, a charge outside the surface will contribute nothing to total flux, since its field lines enter from one side and exit from other. This is the essence of Gauss‟s Law. Q.7
What is Electric Potential Energy? What is the significance of Negative Potential Energy of a System?
Ans.: Electric Potential Energy : When a charged particle or a charge is placed in an electric field a force acts on it in accordance with Coulomb‟s Law, if the charge is now displaced from one position to other, work has to be done against the field or by the field. The energy spent in doing this work is stored as potential energy of the system. This is known as Electric Potential Energy. If an electron is brought near a proton the potential energy will be negative as work will be done by attractive force. Negative Potential Energy means a bound system as work has to be done by external agency to break the system. Q.8
Define Electrical Power and the unit Kilowatt–Hour.
Ans.: Electric Power : Electrical Power is defined as the rate at which electrical energy is consumed or developed. Electrical Power (P) = W / t = VI Its MKS unit is Joule per Second or Watt. Kilowatt-Hour (KWH) : Commercially the consumption of electrical energy is expressed in terms of a unit called KWH.
12
One Kilowatt–Hour (1 unit of electrical energy) is the energy consumed in one hour i.e. 3600 Sec. by a device whose power is one Kilowatt i.e. 1000 Watts. 1 KWH = 3.6 X 106 Joules Q.9
What is the Physical Significance Potential?
Ans.: Definition of Potential : Total work done in moving a unit positive charge from infinity to any point in the electric field is known as the Potential at that point. Vp – V∞ = W / q0 Physical Significance : The level of electric charge in any object is the potential of that object or the level of electric charge at any point is the potential at that particular point.
Multiple Choice Questions
1.
The force of attraction or repulsion between charges follows: (a) Square law of distance (b) Inverse square law of distance (c) Both (a) and (b) (d) None of (a) and (b) ( )
2.
When the distance between two equal charges is decreased to half and their magnitude of charges also decreased to half, the force between them: (a) Remains unchanged (b) Reduces to half (c) Becomes half (d) None of the above ( )
3.
Electric field intensity due to a point charge follows: (a) Falls inversely proportional to the distance (b) Falls inversely proportional to the square root of the distance (c) It does not change with distance (d) Falls inversely proportional to the square of the distance
( )
One volt potential difference is equivalent to: (a) 1 Newton/coulomb (b) (c) 1 Joule/coulomb (d)
( )
4.
1 erg/Coulomb 1 Coulomb/Joule
Electrical Circuit and Circuit Analysis
5.
6.
7.
The Unit of electric field intensity is: (a) Newton/meter (c) Newton/Coulomb
(b) (d)
Coulomb/Newton Joule/Newton
( )
The value of 1 electron volt is: (a) 1.6 X 10–19J (c) 3.2 X 10–19J
(b) (d)
1.6 X 1019J 1.6 X 10–20 J
( )
The energy stored in an capacitor is in the form of: (a) Kinetic energy (b) Potential energy (c)
8.
9.
10
Magnetic energy
Which of the following is not conserved: (a) Mass (c) Total energy
Elastic energy
( )
(b) (d)
Charge Momentum
( )
Erg/Coulomb Coulomb/Joule
( )
What will be the potential energy of the proton-electron system in a hydrogen atom? r is the radius of the orbit of the electron: (a) – Ke/r (b) –Ke2/r +Ke/r
(d)
+Ke2/r
( )
The distance between two charges q1 and q2 is r, and then the electric potential energy of this system will be: (a) (b) (c)
12
(d)
One volt potential difference is equivalent to: (a) Newton/Coulomb (b) (c) Joule/Coulomb (d)
(c) 11
13
(d)
( )
A charge q is placed at a distance of 10 cm from a charge of 8 X 10 –8 C. If the force between the two charges is 0.072 N, the value of q is: (a) 10–3 C (b) 10–5 C (c)
10–6 C
(d)
10–8 C
( )
14
13
If the distance and value of the charges located at different points are doubled, then the force acting between them will be: (a) (c)
14.
15.
Double Unchanged
(b) (d)
Half Four time
( )
The unit for electric field intensity is: (a) Newton/Coulomb (b) Joule/Coulomb (c) Volt-meter (d) Newton/meter ( ) A charge q is placed on the corner of a cube. The flux emerging out of the cube will be: (a) q/ (b) q/ (c) q/ (d) q/ ( )
16
The intensity of an electric field at some point distance r from the axis of infinite long pipe having charges per unit length as q will be: (a) Proportional to r2 (b) Proportional to r3 (c) Inversely proportional to r (d) Inversely proportional to r2 ( )
17
The dielectric constant of aluminum is: (a) 1 (b) Zero (c) 10 (d) Infinity ( ) The charge of same magnitude q are placed at four corners of a square of side a. The value of potential at the centre of square will be: (a) 4kz/a (b) 4
18.
(c) 19
20.
4
(d)
( )
If a soap bubble is positively charged, then its radius: (a) Increases ` (b) Decreases (c) Remain unchanged (d) First increases and then decreases
( )
If a charge Q is brought near another charge Q, then total energy of the system: (a) Remains same (b) Increases (c) Decreases (d) None
( )
Electrical Circuit and Circuit Analysis
15
21
If a positive charge is established in an electric field against the Coulomb force then: (a) Work is done by electric field (b) Energy is utilized from some external sources (c) Intensity of electric field decreases (d) Intensity of electric field increase ( )
22.
A point has 10 volt potential, if a charge of + 10coulomb is brought from infinity to that point, then the work done will be: (a) 10 J (b) 100 J (c) 1J (d) 2J ( ) Which of the following experiment verifies quantization of charge? (a) Rutherford (b) Millikan's oil drop (c) Discharge of gases (d) Faraday's electrolysis ( )
23
24.
25.
26
27.
Which is not a property of conductors? (a) Have free electrons (b) Resistance increases with temperature (c) Negligible bank gap (d) Contains electron - hole pairs
( )
Which is wrong about coulomb's force? (a) It is a long range force (b) it follows inverse square law (c) It does not depend on medium (d) It may be attractive as well as repulsive
( )
Which relation violates the law of conservation of electric charge? (a) n p +e– +v (b) P n + e+ + v + (c) e e (d) e+ e+
( )
A charge + Q is placed at the centre of a cube, the amount of electric flux through its entire surface is: (a) (b) (c)
28.
(d)
Zero
( )
The electrostatic potential energy of a system of two stationary point charges + q1 and - q2 are separated by a distance r is given by: (a) (b)
16
(b)
S.NO. Ans S.NO. Ans S.NO. Ans
Q:1 A 10 A 19 C
(d)
2 B 11 C 20 A
3 C 12 C 21 C
4 C 13 B 22 A
5 C 14 D 23 B
( )
6 A 15 D 24 A
7 B 16 C 25 C
8 B 17 B 26 A
9 A 18 D 27/28 C/B
Electrical Circuit and Circuit Analysis
17
Chapter-2
Capacitors Q.1
Relate Capacity with Voltage and Charge. How it is said that Potential of Earth is zero?
Ans.: When a conductor is charged, its electric level i.e. electric potential rises. The increase in potential is proportional to the charge given to it. If increase in potential is V when charge Q is given to the conductors, then Q OR
Q
V =
CV
- - - (1)
C is constant and is called capacity of the conductor. It depends on the geometry of the conductors, medium around it and nearness of other conductors. From eq.” (1)
C
=
Q /V
Unit of capacity in M.K.S. System is Farad (F) 1 Farad
=
1 Coulomb 1 Volt
As we know that electric potential belongs to electrical level of charge at particular point or in any object. Since the size of earth is very – very large, therefore, the level of charge is also very small thus potential of earth is said to be zero.
Q.2
Describe the factors on which Capacitance of Parallel Plate Capacitor depends.
18
Ans.: Capacity of a Parallel Plate Capacitor is given by C
=
ε0 A / d
Farad
Where ε0
->
Permittivity of air or vacuum
A
->
Area of the plates
D
->
distance between them
From this formula, we see that And
C
A
C
1/d
Therefore, for increasing the capacity, the area of plates must be increased and distance between them be decreased. It means capacity depends on the area of the plates and distance between the plates. Capacity also depends on the dielectric constant of the medium between the plates.
Q.3
What is a Capacitor? Explain its principle.
Ans.: Condenser or Capacitor : The Condenser is an arrangement in which the capacity of a conductor is increased by placing another earthed conductor close to it. A condenser works on the principle that by placing a earthed conductor near a given charge conductor, the potential can be reduced substantially and capacity can be increased.
Electrical Circuit and Circuit Analysis
(i)
19
(ii)
As shown in fig.(i) when we place another conductor (B) near a charged conductor (A), then by induction an opposite charge is induced on the inner surface of B and an equal similar charge is induced on the outer surface. The opposite negative charge on B decreases the potential of A but the similar positive charge on outer surface of B increases the potential of A. This similar charge on B can be removed by connecting outer surface of B to ground. Then potential will decrease more and capacity will increase.
Q.4
Explain Spherical Capacitor.
Ans.: Spherical Capacitor : It consists of two concentric hollow metal spheres, which do not touch each other at any point.
20
Let radius of spheres A and B are rA and rB respectively, where rA < rB. If the inner sphere is given a charge +Q, a charge –Q is developed on inner surface of B and a charge +Q on the outer surface of B, by induction. If air is the medium between spheres, the potential on the surface of A due to charge +Q on it is VA
=
1
Q
4пε0
rA
Similarly, the potential on the surface of A due to charge -Q on B is VB
=
1
-Q
4пε0
rB
1
Q
4пε0
rA
So, resultant potential of A is V
=
VA - VB
= =
-
Q
(rB – rA)
4пε0
rA r B
1
-Q
4пε0
rA
Electrical Circuit and Circuit Analysis
21
Therefore capacity of Spherical Capacitor C
=
Q
=
Q x 4пε0 rA rB
V C
Q.5
=
Q (rB – rA) 4пέ0
rA rB (rB – rA)
Describe Series Combination of Capacitors. Explain relation between Equivalent Capacitance and Smallest Capacitance in the combination.
Ans.: Series Combination of Capacitors :
V In Series Combination, the first plate of the first condenser is connected to the source of charge and second plate of the last condenser is connected to second terminal of source or is earthed. The second plate of first condenser is connected
22
to first plate of second condenser; the second plate of second condenser is connected to first plate of third condenser and so on as shown in figure. The potential difference across these condensers depends on the capacities of these condensers. Suppose the values of potential difference across C1, C2 and are C3 are V1, V2 and are V3 respectively. So
V1
=
Q
, V2
=
C1
Q
&
V3
C2
=
Q C3
If total potential difference is V then V
=
V1
+
V2
+
V3
=>
=
Q
+
Q
+
Q
C1 =>
V
=
Q =>
1 C
C2 1
+
C1 =
1
C3 1
+
C2 +
C1
1 C2
1 C3
+
1 C3
Where C is resultant capacity. The resultant Series Capacitance is always less than the Smallest Capacitance in the combination.
Electrical Circuit and Circuit Analysis
Q.6
23
Describe Parallel Combination of Capacitors.
Ans.: Capacitors in Parallel :
In this combination first plate of all capacitors are joined at one point which is connected to one terminal of the source, the second plate of all capacitors are joined at another point which is earthed or connected to the second terminal of the source. If the charge given by the source is +Q, this charge is distributed on the condensers in parallel according to their capacities as potential difference V is same for all. If the amount of charge received by the condensers are Q1 , Q2 and Q3 then Q
=
Q1
+
Q2
+
Q3
=>
Q
=
C1 V
+
C2 V
+
C3 V
=>
Q
=
V(C1 +
C2
+
C3 )
=>
Q /V =
C1
+
C2
+
C3
=>
C
C1
+
C2
+
C3
=
Where C is equivalent capacity.
24
In Parallel Combination, the Resultant Capacitance is more than the capacitances of Individual Capacitors. Q.7
What is a Gang Condenser? Explain its construction and working.
Ans.: Gang Condenser : It is a special type of Plate Condenser. It consists of two groups of semicircular parallel plates.
The alternative plates are connected to one rod A and the other plates to another rod B. One group of plates remains stationary but the other can be rotated with the help of knob. By rotation of one set of plates the overlapping area of the plates can be varied. The two groups of plates form a combination of condensers in parallel. By changing their effective area, the resultant capacitance can be varied. It the effective area of each plate is A and n plates have been used then the resultant capacity. C
=
(n – 1) ε0A D
Where d is the distance between successive plates.
Electrical Circuit and Circuit Analysis
Q.8
25
What is the effect of placing a Dielectric Medium between the Plates of a Capacitor?
Ans.: When dielectric material placed between the charged plates of a capacitor, the centres of negative and positive charge distributions in the atoms or molecules no longer remain coincident but get separated. The centre of negative charge distribution gets displaced towards the positive plate and centre of positive charge distribution towards the negative plates. This phenomenon is called Polarization. Due to this polarization, negative charge gets accumulated on the surface of dielectric near the positive plate and an equal positive charge appears on the surface of dielectric near the negative plates. This accumulation of charge on the two surfaces of dielectric reduces the applied electric field. If the dielectric constant of the medium is K then the electric field intensity between the charged plates of a parallel plate condenser becomes. EK
=
σ ε
=
σ ε0K
And due to this capacity of dielectric filled capacitor is K times, the capacity in air or vacuum. Where
Q.9
Cm
=
KC
C
=
ε0A d
Farad
A Parallel Plate Capacitor of plate area A and separation of is filled with two materials each of thickness d/2 and dielectric constants ε 1 and ε 2 respectively. What is its equivalent capacitance?
Ans.: Formula :
26
C
=
Q
=
V
ε0A t1
+
k1
t2 k2
Here t1 & t2 are thickness and k1 & k2 are dielectric constants. In this question and So,
C
t1
=
t2
=
d/2
k1
=
ε1
&
k2
=
=
ε2
ε0A d/2
+
ε1 =
d/2 ε2
ε0A d
1
2
ε1
=
+
1 ε2
2ε0A d
ε2
+
ε1
ε1 ε2 =>
C
=
2ε0A d
ε1 ε2 ε1
+
ε2
Multiple Choice Questions Q:01 A parallel plate capacitor is given a charge Q. If the separation between the plates is doubled, its capacity will be: (a) unchanged (b) Zero (c) doubled (d) half ( ) Q:02 In a charged capacitor the energy resides:
Electrical Circuit and Circuit Analysis
(a) (b) (c) (d)
27
on the positive plate on both the positive and negative plates in the field between the plates around the edge of the capacitor plates
( )
Q:03 In a charged capacitor the energy appears as: (a) magnetic energy (b) electromagnetic energy (c) electrostatic energy (d) neither electric nor magnetic
( )
Q:04 Two condensers of capacitor C1 and C2 charged to potential V1 and V2 are joined by a wire. The loss of energy E is: (a) E = (C1 + C2) (V1–V2)2 (b) (c)
(d)
Q:05 On heating the dielectric constant of an insulator: (a) remains constant (b) (c) decreases (d)
increase nothing can be predicted
( )
Q:06 A charge on each capacitor in the circuit is : 1 F
4V
IV ++ 2+ + F
+ + (b) (a) 1 C 2 C (c) 3 C (d) 4 C ( ) Q:07 If dielectric medium of constant K is filled between the plates of a capacitor, then its capacity increases: (a) times (b) k times (b) K2 times (d) Q:08 The energy stored in an capacitor is in the form of: (a) Kinetic energy (b) Potential energy
( )
28
(c)
Magnetic energy
(d)
Elastic energy
( )
Q:09 The capacitance of a capacitor does not depend upon: (a) Shape of plates (b) Size of Plates (c) Charge on plates (d) Separation between plates
( )
Q:10 A 4 µ F capacitor is charged to 400 V. The energy stored in it will be: (a) 0.16 J (b) 0.32 J (c) 0.64 J (d) 1.28 J
( )
Q:11 Four capacitor each of capacity 3 Farad are connected in series. The resultant capacity will be: (a) (b) (c)
(d)
Q:12 A parallel plate capacitor is given a charge Q. capacity will be: (a) Halved (b) (c) Zero (d) Q:13 A capacitor stores energy in the form of : (a) Electromagnetic field (b) (c) Electric Field (d)
( ) If the area of plates is doubled, its Doubled Unchanged
( )
Magnetic field None of the above
( )
Q:14 The capacitances of two capacitors are C1 and C2 It ehy charged to the same potential, then the ratio of their charges will be: (a)
(b)
(c)
(d)
Q:15 Unit of capacitance is: (a) Coulomb (c) Henry Q:16 Two capacitors of capacitances 2 equivalent capacitance will be: (a) 6 F (c)
F
(b) (d) F and 4
( )
Volt Farad
( )
F are connected in series. Their
(b)
2
F
(d)
8
F
( )
Electrical Circuit and Circuit Analysis
29
Q:17 On heating the dielectric constant of an insulator: (b) remains constant (b) (c) decreases (d) ( )
increase nothing can be predicted
Q:18The equivalent capacitance of the circuit between A and B is: (a)
3C
A
F
C µF
C µF B
(b) C µF
(c) (d)
( ) . Q:19 When dielectric material is inserted between the plates of a capacitor its capacitance (a) decreases (b) increase (c) ions constant (d) reduces to zero
S.NO. Ans S.NO. Ans
Q:1 D 10 A
2 B 11 A
3 C 12 B
4 D 13 C
5 A 14 D
6 A 15 D
7 B 16 C
8 B 17 B
9 A 18 D
30
Chapter-3
Current Electricity Q.1
State Ohm’s Law.
Ans.: Ohm’s Law : This law states that if the physical conditions of a conductor (such as temperature, pressure etc. remain same, then the current flow through it is directly proportional to the potential difference applied across it. Therefore, if V is the potential difference across the ends of a conductor and I is the current flowing through it, then i.e.
V
I
=>
V
=
RI
=>
V
=
R
(Constant)
I This constant is known as resistance of the conductor.
(Graph between applied Potential Difference V and Current I) Q.2
Define Resistance of a Conductor. On what factors and how does the Resistance of a Conductor depend?
Electrical Circuit and Circuit Analysis
31
Ans.: The obstruction produced in the motion of free electrons is called Electrical Resistance of Conductor. R = V/I Practical unit of resistance is Ohm. If the potential difference across the ends of a conductor is one volt and the current flowing through it is one ampere, then the resistance of the conductor is one Ohm. Resistance of a Conductor depends on the following factors : (i)
Length of the Wire : The resistance of a conducting wire is directly proportional to its length i.e. R
(ii)
l
Cross Sectional Area or Thickness of the Wire : The resistance of the wire is inversely proportional to cross sectional area of the wire i.e. R
(iii)
α
l/A
Material of the Wire : If wires of same length and same thickness are made from different materials, then their resistance will be different. Thus if the length and cross-sectional area of the wire are l and A respectively, then the resistance R =>
α R
l/A =
ρ l/A
Where ρ is a constant, called the Specific Resistance or Resistivity of the material of the wires. Q.3
Define Specific Resistance. Why alloys as manganin and constantan are used to make resistance wires of resistance?
Ans.: We know that R
=
ρ l/A
Where ρ is called the Specific Resistance or Resistivity of the material of the wire. From the above relation if
l
=
1 metre
and
A
=
1 m2
32
Then R
=
ρ
Thus the resistivity or specific resistance of the material of a wire is equal to the resistance of a wire of that material having a length of 1 metre and cross sectional area of 1 m2. Unit of specific resistance is Ohm – m. The resistivity of alloys also increases with the rise of temperature. There are certain alloys such as manganin and constantan for which effect of temperature is very small because of their negligible temperature coefficient of resistance. On account of their high resistivity and negligible temperature coefficient of resistance these alloys are used to make resistance wires for resistance boxes, potentiometers, meter bridges etc. Q.4
Difference between EMF and Terminal Voltage.
Ans.: Electromotive Force (E) : The EMF of a cell in a closed circuit is equivalent to the work done for the flow of unit positive charge through the external and internal resistance. Terminal Voltage (V) : Terminal voltage is equivalent to the work done for the flow of unit positive charge through the external resistance only. E is always greater than V and their difference is equal to the potential drop across the interval resistance of the cell. E - Ir = V Or we can say that the EMF (E) is the amount of work done in driving a unit positive charge around the whole circuit (external and internal) while the potential difference (V) in the closed circuit is the amount of work done in driving a unit positive charge through the external resistance only. Q.5
Explain the Series and Parallel Combination of Resistance.
Ans.: Series Combination of Resistances : In this combination, the second end of the first resistance is connected to first end of the second resistance and so on. In such a combination, same amount of current flows in all resistance but the potential difference across the resistance changes according to their resistance.
Electrical Circuit and Circuit Analysis
33
Let i is the current flowing through R1, R2 & R3, then by Ohm‟s law V1
=
i R1 ,
V2
=
i R2
and
V3
=
i R3
If total potential difference applied by the battery is V, then V
=
V1
+
V2
+
V3
=
i R1
+
i R2
+
i R3
=
i (R1
+
R2
+
i R3 )
(1)
If the equivalent resistance of the combination is R, then by Ohm‟s law V
=
iR
(2)
Comparing equations (1) and (2) iR
=
i( R1
+
R2
+
R3 )
R
=
R1
+
R2
+
R3
Thus the equivalent resistance of resistances connected in series is equal to sum of individual resistance. Parallel Combination of Resistances : In this combination one end of all resistances are connected together at one point and other end of all resistances are connected together at another point.
34
Suppose the current supplied by the battery is i, this current is divided into three parts, i1 flowing through R1, i2 flowing through R2 and i3 flowing through R3. i = i1 + i2 + i3 If the potential difference between A and B is V, then i1
=
V
,
i2
=
R1
V
&
i2
R2
=
V
+
R1 =>
i
=
i
=
V 1
V =>
1
1
1 +
1
1
+
1
1 R3
+
R2 +
V R3
R2
R1 =
+
R2
R1 =>
V
V R3
Using these values i
=
1 R3
+
1
Electrical Circuit and Circuit Analysis
R
35
R1
R2
R3
Thus the reciprocal of the equivalent resistance of the resistances connected in parallel is equal to the sum of the reciprocals of individual resistances. Q.6
What is the need of Kirchhoff’s Laws? Explain Kirchhoff’s Current Law with the help of examples.
Ans.: Need of Kirchhoff’s Law : Ohm‟s Law gives the relation between the potential differences across a conductor and the current flowing through it. In complex circuits i.e. electrical networks direct use of Ohm‟s Law is not possible. Therefore to determine the current flowing through any branch of network and the voltage at the node, Kirchhoff‟s Laws are used. Kirchhoff’s Current Law : According to this law the algebraic sum of the currents meeting at any junction or node is zero i.e. ∑i
=
0
The current towards the junction are taken as positive and going away from the junction are taken as negative. So applying Kirchhoff‟s Law in this figure i1 – i2 – i3 - i4 + i5 = 0 OR
i1 + i5 = i2 + i3 + i4
Example : In this figure to find out the value of i, we apply Kirchhoff‟s Current Law 5 + 7 + 2 - 3 - i= 0 =>
11 – i = 0
=>
i = 11 Amp.
5 3 7 2 i
36
Q.7
Explain Kirchhoff’s Voltage Law with help of examples.
Ans.: Kirchhoff’s Voltage Law : According to this law, the algebraic sum of the voltages in a specified direction along a closed loop of an electrical circuit is zero. ∑∆v
=
0
We adopt the following sign conventions : (i)
The EMF of a cell is taken negative if we move in the direction of increasing potential (i.e. from –ve pole to +ve pole) through the cell and is taken +ve if we move in the direction of decreasing potential (i.e. from +ve pole to –ve pole) through the cell.
(ii)
The voltage drop across any resistance will be +ve if these are in the direction of current flow. Using these two conditions and starting from point A OR
V1
+
V2
+
E2
-
E1
V1
+
V2
=
E1
-
E2
=
0
Thus the algebraic sum of all the voltage drops in a closed loop is equal to the sum of EMFs in the loop. Q.8
Explain Charging of Capacitor.
Ans.: Charging of Capacitor : In this circuit when we close the key k, let q be the charge on capacitor at time t and I be the current in the circuit.
Electrical Circuit and Circuit Analysis
37
The potential difference across capacitor will be q/c. Using Kirchhoff‟s Voltage Law E
=
q
+
RI
(1)
C
As time increases the charge on the capacitor increases and finally acquires the maximum value q0. At this state, potential difference across capacitor becomes equal to EMF (E), thus E
=
q0
(2)
C Putting this in equation (1) q0
=
C
q
+
RI
―
RCI
(q0
-
q)
(q0
-
q)
(q
-
q0)
C
Or
q
=
q0
Or
I
=
1 RC
Or
dq
=
dt Or
dq
1 RC
=
−1
(3)
38
dt =>
RC dq
(q
-
= q0)
-1
dt
RC
Integrating eqn (3) Loge(q
-
q0)
=
-1
t
+
C1
-1
t
RC Now at t = 0, q = 0 So,
loge ( - q0 )
=
C1
By putting this value of C1
Loge(q
-
q0)
-
loge ( - q0 )
=
RC Loge q
-
q0
=
-1
- q0 q
-
t RC
q0
=
-1
- q0
t
RC
q
-
q0
q
=
q0(1
- q0 e – t/RC
=
-
e – t/RC)
Electrical Circuit and Circuit Analysis
Q.9
39
Explain Discharging of a Capacitor.
Ans.: Discharging of a Capacitor : Capacitor is discharged through a resistance R by closing key k2 (keeping k1 open. Let q be the charge on the capacitor at time t and I be the current flowing through R at this moment. The initial charge on capacitor is q0 = EC. During discharging process as E=0, so by Kirchhoff‟s Law
q
+
RI
=
0
q
=
0
(1)
C OR
R dq + dt
OR
dq
C =
dt OR
dq
-1
q
RC =
q
-1
dt
(2)
RC
Integrating eqn (2) Loge q
=
-1 RC
At t = 0, q = q0 = EC So,
B
=
Loge (q0)
dt
+
B
40
Substituting the value of B Loge q
=
-1
dt
+
Loge q0
=
-1
RC Loge q
-
Loge q0
t
RC Loge q
=
q0 q
-1
t
RC =
q0 e – t/RC
Thus the charge on capacitor decreases exponentially with time t as shown below.
Q.10 What is Time Constant of an RC Circuit. Ans.: Time Constant of an R-C Circuit : In an R-C circuit, the growth of charge and potential difference across the capacitor during charging or discharging are dependent on time. During both these processes maximum current flows at the start and then the current decays exponentially with time. The rate of variation of all these quantities (charge, potential and current) infact depends on the value of time t relative to the product RC. The product RC has the dimensions of time and is called Time Constant of the circuit and is represented by τ. During charging
Electrical Circuit and Circuit Analysis
and
41
q
=
q0 (1
-
e– t/τ )
I
=
I0 e – t/τ
q
=
q0 e – t/τ
I
=
- I0 e – t/τ
q
=
q0 (1
-
e– 1 )
q
=
q0 (1
-
0.37 )
q
=
0.63 q0
I
=
0.37 I0
During discharging and
At t = τ during charging
and
i.e. time constant is the time at which during charging the charge on capacitor increase about 63% of the maximum value while current decreases to 37% of the maximum value.
Multiple Choice Questions Q:01 The energy stores in an inductance coil is given by: (a)
(b)
(c)
(d)
Q:02 Two resistances of 0.275 ohm and 0.778 ohm resistance shall be: (a) More than 0.275 ohm (b) (c) Equal to 1.053 ohm (d) Q:03 The specific resistance of a wire depends upon: (a) Its length (b) (c) Its dimensions (d)
LI2
( )
are connected in parallel. The total Less than 0.275 ohm More than 0.778 ohm
( )
Its cross-section area Its material
( )
42
Q:03 When two resistances are connected in series, they have: (a) Same voltage (b) Same resistance (c) Same current (d) Different current
( )
Q:04 Unit of resistivity is: (a) ohm/meter (c) ohm-meter
( )
ohm/meter2 ohm-meter2
(b) (d)
Q:05 Kirchhoff's first low is related to the law of: (a) Conservation of energy (b) Conservation of charge (c) Conservation of mass (d) Conservation of angular momentum Q:06 The conductivity of superconductor is : (a) Infinite (c) Very small
( )
(b) (d)
Very large Zero
( )
Q:07 The current i in the given circuit is:
2V
+ -
30
30
30
(a)
(b)
(c)
(d)
Q:08 The example of non-ohmic resistance is: (a) Copper wire (c) Diode Q:09 The resistance of a conductor depends on: (a) Its length only (c) Its temperature Q:10 Unit of potential difference is:
( )
(b) (d)
Carbon wire Tungsten wire
( )
(b) (d)
Its cross - sectional area All of the above
( )
Electrical Circuit and Circuit Analysis
(a) (c)
43
Volt Joule
(b) (d)
Ampere Coulomb
( )
11
The diameters of two resistance wires of equal length and of the same material are in the ratio of 1 : 2 the ratio of their resistances will be: (a) 1:2 (b) 1:4 (c) 4:1 (d) 2:1 ( )
12.
The conductivity of a superconductor is: (a) Zero (c) Large
(b) (d)
Unit of resistivity is : (a) ohm/m (c) ohm-m
(b) ohm/m2 ohm-m2
13
14.
15.
16
17.
18.
Q:19
(d)
Small Infinite
( )
( )
In a closed circuit, kirchhoff's second law represents: (a) ohm's law (b) Charge - conservation law (c) Current-conservation low (d) None of the above
( )
The charging current in R-C circuit varies with time I as: (a)
I = Ioe
(b)
I = Ioe
(c)
I = Io 1 - e -
(d)
I = Io 1 + e
( )
The resistance of straight conductor does not depend on its: (a) Temperature (b) Length (c) Material (d) Shape of cross-section
( )
The unit of specific conductance is: (a) Ohm (c) Siemen
(b) (d)
Ohm-M mho-m
( )
The example of non-ohmic resistance is: (a) Copper wire (c) Diode
(b) (d)
Carbon wire Tungsten wire
( )
A flow of 107 electrons per second in a conducting wire constitutes a current of:
44
(a) (c) Q:20
Q:21
1.6 X 10–26 A 1.6 X 10–12 A
(b) (d)
1.6 X 1012 A 1.6 X 1026 A
( )
Indentify the set in which all the materials are good conductors of electricity. (a) Cu, Ag and Au (b) Cu, Si and diamond (c) Cu, Hg and NaCL (d) Cu, Fe and Hg
When a current flows in a conductor, the order of magnitude of drift velocity of electrons through it is: (a) 1010 m/s (b) 10–2 m/s (c)
1010 cm/s
(d)
10–7 cm/s
( )
Q:22. The temperature co-efficient of resistance is positive for: (a) Carbon (b) Copper (c) Si (d) Ge Q:23
( )
( )
The temperature co-efficient of resistance is negative for: (a) Ge (b) Copper (c) Aluminum (d) Nickel
Q:24. The example of non-ohmic resistance is: (a) Copper wire (c) Diode
(b) (d)
( )
Carbon resistance Tungsten wire
( )
S.No
Q:1
2
3
4
5
6
7
8
9
Ans
B
C
C
C
B
B
C
B
D
S.NO.
10
11
12
13
14
15
16
17
28
Ans
A
C
C
C
C
C
D
A
B
S.NO.
19
20
21
22
23
24
Ans
C
A
B
A
C
Electrical Circuit and Circuit Analysis
45
Chapter-4
Magnetism Q.1
Obtain an expression for the Magnetic Induction due to a Bar Magnet at a point on its axis.
Ans.: Magnetic Induction due a Bar Magnet at a point on its axis :
Let a point P on its axis at a distance r from its centre. The distance of point P from the N – Pole will be (r – l) while from S – Pole it will be (r + l). The magnetic field intensity at P due to N – Pole will be μ0
m
4П
(r – l)2
and due to S-Pole it will be μ0
m
4П
(r + l)2
46
So, resultant magnetic field intensity at P is B
B
=
μ0
m
4П
(r - l)2
=
μ0
m(r + l)2 - m(r - l)2 4П (r2 - l2)2
=
μ0
4mlr
4П
(r2 - l2)2
μ0
2Mr
4П
(r2 - l2)2
=
-
m
along the axis
(r + l)2
(where M = 2ml)
For a short magnet r > > l, so l2 will be negligible compared to r2. = B
Q.2
=
μ0
2Mr
4П
r4
μ0
2M
4П
r3
Obtain an expression for the Magnetic Induction due to a Bar Magnet at a point on its equatorial line.
Ans.: Magnetic Induction due to a Bar Magnet at a point on its equatorial line:
Electrical Circuit and Circuit Analysis
47
Consider point P on equatorial line of magnet at distance r from its centre. The distance of P from both the poles will be the same, equal to (r2 + l2)1/2 The intensity of magnetic field due to N – Pole will be B1
=
μ0
m
along PQ
4П
(r2 + l2)
The intensity of magnetic field due to S – Pole will be B2
=
μ0
m
along PR
4П
(r2 + l2)
The components of B1 & B2, which are perpendicular to the axis being equal and opposite, will cancel each other while the components parallel to the axis being in the same direction will get added. So, resultant magnetic field at P will be in a direction parallel to the axis and will be given as B
=
B1 Cosθ
B
=
μ0 4П
= =
μ0
+ 2m
Cosθ
(r2 + l2) 2m
4П
(r2 + l2)
μ0
M
4П
B2 Cosθ
l (r2 + l2)1/2 (where M = 2ml)
(r2 + l2)3/2
For a small magnet l < < r, so that B
Q.3
=
μ0
M
4П
r3
State Biot-Savart’s Law.
Ans.: Biot – Savart’s Law : This law is used to determine the magnetic field intensity at a certain point.
48
This law states that magnetic field intensity δB at a certain point due to a current carrying element
δl of the conductor is (i)
directly proportional to current I.
(ii)
directly proportional to length δl of the current element.
(iii)
directly proportional to Sinθ, where θ is angle between the position vector r of the point of observation with respect to the element and the element δl
(iv)
inversely proportional to the square of the distance r of the observation point from the element, i.e. δB
I δl Sinθ r2
In free space or non magnetic medium δB Where
=
μ0
I δl Sinθ
4П
r2
Tesla
μ0 = Permeability of free space = 4П x 10-7 Weber/A-m
For other media μ is used in place of μ0 for the permeability of that medium.
Electrical Circuit and Circuit Analysis
Q.4
49
Obtain an expression for the Magnetic Induction at the Centre of a Current Carrying Coil.
Ans.: Magnetic Induction at the Centre of Coil due to Circular Current Carrying Coil : As shown in figure, the distance of observation point (centre) from each element of the coil is equal to the radius „a‟. In addition the position vector r makes an angle of 90˚ with each element. Hence Sinθ = Sin90˚ = 1. Thus from Biot-Savart‟s Law. The magnetic induction due to a current carrying element δl at the point P
δB
=
μ0
Iδl
4П
a2
The direction of magnetic field due to all the elements is same. Therefore total magnetic induction at the centre of the coil is B
=
ΣδB
=
μ0
I
4П
a2
μ0
I
4П
a2
= B
=
μ0I
Σδl (2Пa)
50
2a If the coil has n turns, then Σδl
=
2Пan
B
=
μ0nI
Tesla
2a Q.5
Determine the Force per unit length between Two Current Carrying Parallel Conductors.
Ans.: Force between Two Current Carrying Parallel Conductor : Let two infinately long parralel conductors separated by distance „d‟. Let i a & ib are the currents in these conductors. These conductors are formed to exert force on each other. It is confirmed experimentally that mutual force is attractive when current in those conductors flow in the same direction but repulsive when current in the conductors are in opposite direction.
The magnetic field produced by current „ia‟ flowing in the wire „a„ at a distance „d‟ is Ba
=
μ0ia
Electrical Circuit and Circuit Analysis
51
2Пd According to Right Hand Palm rule, field Ba is perpendicular to the plane of paper and directed downwards. This means that second current carrying conductor is now placed in field B a hence it will experience a force due to Ba. The magnitude of this force Fb on the element δl of wire will be Fb
=
ib δl Ba
Fb
=
μ0
ia ib δl
2П
d
This direction of Fb will be towards conductor a. Thus the force per unit length of wire „b‟ Fb
=
δl
μ0
ia ib
2П
d
Similarly force per unit length of wire „a‟ due to the magnetic field produced by wire b will be Fa
=
δl Q.6
μ0
ia ib
2П
d
Define Magnetic Flux. State Faradey’s Laws of Electromagnetic Induction.
Ans.: Magnetic flux : The magnetic flux Φ linked with any surface placed in magnetic field B is measured by total number of magnetic lines of force passing through it. If we imagine that a plane surface of area A is placed in uniform magnetic field (In which lines of force are parallel and equidistant) then magnetic flux Φ is given as Φ
=
B.A =
BACosθ
Where θ is the angle between area vector & magnetic field. Faraday’s Laws of Electromagnetic Induction :
52
Q.7
(i)
Faraday’s First Law : Whenever the magnet flux linked with a circuit changes with time an induced EMF is developed in the circuit. The induced EMF in the circuit exists so long as the change in magnetic flux continues. This law gives the cause of generation of induced EMF.
(ii)
Faraday’s Second Law : The magnitude of induced EMF in a circuit is equal to the rate at which the magnetic flux linked with the circuit changes.
State Lenz’s Law with suitable example.
Ans.: Lenz’s Law : The direction of induced EMF and induced current is obtained with the help of this law. According to this law the direction of induced current in the circuit is always such that it opposes the very cause which has produced it. This law is applicable to closed circuits only. Suppose a bar magnet SN is pushed towards the coil then induced EMF must oppose the motion of magnet towards the coil. A north pole is formed at the face of the coil opposite to magnet and magnet is repelled. And when viewed from the side of magnet, the current in coil is anticlockwise.
Similarly when the magnet is moved away from the coil, a south pole is formed at the opposite face and the attractive force between south and north poles opposes the motion, therefore, the current in the coil will be clockwise. Q.8
Explain Phenomena of Dia, Para and Ferromagnetic Materials.
Ans.: Diamagnetic Substances : Those materials which are repelled by magnetic field i.e. a force acts on them from higher magnetic field region (in opposite direction) such as water, sodium chloride etc. are called Diamagnetic Substances.
Electrical Circuit and Circuit Analysis
53
Paramagnetic Substances : Those materials which experience a magnetic field i.e. the force acts from weaker magnetic field region are called Paramagnetic Substances. The force acting on the substances is very small in comparison to the force on the substances as iron, nickel etc. Ferromagnetic Substances : The substances such as iron, nickel and cobalt experience a strong force of attraction by magnetic field and are called Ferromagnetic Substances. If a small bar of a substance is suspended between the poles of a magnet, then diamagnetic substance tends to align perpendicular to the magnetic field, paramagnetic substance tends to align parallel to the magnetic field and ferromagnetic substance tends to align to the magnetic field even by weak field. Q.9
Show the dependence of Magnetic Susceptibilities of Dia, Para and Ferromagnetic Materials on Temperature.
Ans.: Magnetic Susceptibility (X) is a property which determines how easily a magnetic material can be magnetized. Magnetic susceptibility of diamagnetic substances does not depend on the temperature since motion of electrons does not depend upon the temperature. Magnetic Susceptibilities of Paramagnetic Substances depend upon the temperature and according to Curies‟ law the magnetic susceptibility X of Paramagnetic Substance is given as X =>
X
1/ T =
C/T
C is called Curie’s Constant Magnetic Susceptibility of Ferromagnetic materials depends upon temperature. Its dependence on temperature is according to Curie – Weiss Law and given as X
=
C T - Tc
Where Tc is called Curie Temperature
54
Curie Temperature is that temperature at or below which a material behaves like a ferromagnetic material and above which it behaves like a paramagnetic material. Q.10 Define Self Induction and Mutual Induction. Ans.: Self Induction :
Due to change in current passing through a coil, the magnetic field produced by it and the magnetic flux linked with it changes with time, producing an induced EMF in the coil. This phenomena is called Self Induction. The phenomena of self induction occurs in every current carrying circuit or element. Mutual Induction : The phenomena of electromagnetic induction in which, on changing the current in one coil an opposing induced EMF is produced in a neighboring coil, is known as Mutual Induction.
Multiple Choice Questions 1 Magnetic induction due to a solenoid of length ‘L’ radius R, no. of turns N and current I is: (a) (b) (c)
(d)
( )
Electrical Circuit and Circuit Analysis
2
3.
4
5
6
7
The unit of magnetic flux density is: (a) Weber/m (c) Weber/m2
9
(b) (d)
Weber amp/m
( )
The commercial unit of electrical energy is: (a) Joules (b) Watt (c) Kilowatt (d) Kilowatt hour ( ) The magnetic induction at the centre of a circular current carrying coil of redius 'r" is: (a) µOni (b) 2µOni 2a a (c) µOni (d) Zero ( ) a The rays which remain unperfected in a magnetic field are: (a) (c)
(b) (d)
Positive rays
( )
The cause of diamagnetism is: (a) Orbital motion of electrons (c) Paired electrons
(b) (d)
Spin motion of electrons None of the above
( )
A bar magnet of magnetic moment 'M' is cut into two equal parts. The magnetic moment of either of part will be: (a) 2M (b) (c)
8
55
(d)
Zero
( )
The coefficient of self induction of a coil is given by: e (a) L= (b)
L=–
(c)
L=–
L=
(d)
( )
The peak value of a.c. is 4 Ampere the root mean square value of current in the circuit is: (a) 4 Ampere (b) Ampere
56
(c)
Ampere
(d)
8 Ampere
( )
10
Magnetic field is produced by the flow the current in a straight wire. This phenomenon is based on: (a) Faraday's (b) Maxwell's law (c) Coulomb's law (d) Biot-Sawart law ( )
11
Unit of magneto motive force is: (a) Ampere/meter (c) Ampere
(b) (d)
Ampere-meter Weber-meter
( )
12.
The direction of lines of force of magnetic field produced due to flow of direct current in a conductor is formed by: (a) Lenz/s law (b) Right hand rule (c) Faraday's law (d) Biot-svart's law ( )
13
Who discovered magnetic effect of current? (a) Faraday (b) (c) Ampere (d)
Oersted Bohr
( )
14
The value of magnetic induction B at different points situated on the axis of current carrying wire will be: (a) Zero (b) Maximum (c) Proportional to current (d) None of above ( )
15
The field intensity due to current I flowing through a straight long wire is proportional to: (a) I (b) I2 (c)
16
17.
When will. (a) (b) (c) (d)
(d)
I/I
( )
current is passed, through two long straight wires in same direction then there be force of repulsion between the wires be force of attraction between the wires Not be any force of attraction between the wires Not be any force in opposite direction mutually
The current flowing in opposite direction mutually. (a) Attract each other
( )
Electrical Circuit and Circuit Analysis
(b) (c) (d) 18
19
57
Repel each other do not affect each other Attract sometimes and repel sometimes
The value of magnetic induction inside a solenoid along the radius: (a) Is zero (b) decreases with distance from the axis (c) is uniform (d) increases with distance from the axis
( )
( )
The formula for magnetic induction at the centre of current carrying circular coil of radius r is: (a)
(b)
(c)
(c)
2
( )
20
A circular coil A and radius r carries a current I. Another circular coil B of radius 2r carries a current 2I. The magnetic fields at the centers of the circular coils are in the ratio of: (a) 4 :1 (b) 3:1 (c) 2 :1 (c) 1:1 ( )
21
Magnetic field do not interact with: (a) Stationary electric charges (b) Moving electric charges (c) Stationary permanent magnets (d) Moving permanent magnets `
( )
Diamagnetism is: (a) Distortion effect (b) Orientation effect (c) Both distortion and orientation (d) Cooperative phenomena
( )
The permeability of a substance is zero. Then it is: (a) Diamagnetic (b) Paramagnetic (c) ferromagnetic (d) anti ferromagnetic
( )
22.
23
58
S.NO.
Q:1
2
3
4
5
6
7
8
9
Ans
D
B
D
A
C
A
B
A
C
S.NO
10
11
12
13
14
15
16
17
18
Ans
D
D
B
A
C
A
A
A
C
S.NO
19
20
21
22
23
Ans
C
A
A
C
C
Electrical Circuit and Circuit Analysis
59
Chapter-5
Alternating Current Q.1
Define Electric Current. Differentiate between Direct Current and Alternating Current.
Ans.: Electric Current : The amount of charge flowing per second at a given point or rate of flow of charge is called Current. The practical unit of current is Ampere and is equivalent to Coulomb per Second. When one coulomb charge flows in one second, the current is one Ampere. Direct Current or DC : The current whose magnitude remains constant with time and which flows continuously in a definite direction is call Direct Current.
(I) Current time (t) Alternating Current or AC : The current whose direction is not definite but reversed after definite intervals of time is called Alternative Current or AC. The magnitude of such a current does not remain constant but changes periodically with time.
60
Q.2
Give the Principle of AC Generator. Describe its main parts. What factors does the EMF developed depend?
Ans.: Principle of AC Generator : The working of generator is based on phenomenon of electromagnetic induction i.e. magnetic flux linked with a coil changes, an EMF is induced in the coil. Essential Parts of AC Generator are : i)
Armature
ii)
Field Magnets
iii)
Slip Rings
iv)
Brushes
Armature : This is a rectangular coil. It consists of a large no. of insulated copper wire wound over a laminated soft iron core. The coil can be rotated around the central axis. Field Magnets : N & S are two poles pieces of a strong electromagnet in which the armature coil is rotated. Axis of rotation is perpendicular to magnetic field lines. Slip Rings : These are two hollow metallic rings to which two ends of armature coil are connected.
Electrical Circuit and Circuit Analysis
61
Brushes : These are two flexible metallic plates or carbon rods. The purpose of brushes is to pass on current from the armature coil to external load resistance. Induced EMF in AC Generator is gives as E
=
NABW Sinwt
N ->
No. of turns in coil
A ->
Cross Sectional area of each turn of coil
B ->
Magnetic Field
W -> Angular Velocity of the coil These four are the factors on which EMF depends. This is maximum when Sinwt
=
Maximum
=
1
EMax
=
E0
NABW X 1
Therefore, E Q.3
=
=
E0Sinwt
Define Mean, Peak and RMS Values of an AC and obtain expression for these.
Ans.: Mean or Average Value of AC Current : The mean of the instantaneous value (I = I0Sinwt) over a full cycle is called Mean or Average Value. In a full cycle the mean value of alternating current is zero because during first half of the cycle, the current is positive and in a certain direction and in the next half cycle, the current is negative i.e. opposite to the values in first half cycle. Peak Value (I0) : The maximum value of current in a cycle of alternating current is called Peak Value. Root Mean Square Value : The square root of the mean of square of current over a full cycle is called Root Mean Square Value i.e. RMS Current Irms
=
I2
½
Since the square of the instantaneous value of alternating current is always positive, the RMS Value is never zero. As we know I
=
I0Sin(wt + )
I2
=
I02Sin2 (wt + )
62
Mean value of Sin2 (wt + ) is ½.
Q.4
So,
I2
=
I02 (½)
Hence,
Irms
=
I2
Irms
=
0.707 I0
½
=
I02 / 2
=
I0 / 2
Explain Impedance and Reactance of A.C. Circuit.
Ans.: Impedance : In an AC circuit usually current and potential difference are not in same phase. To obtain a complete relationship between potential difference and current, it is necessary to write the phase difference between potential difference and current along with ratio of magnitudes of these quantities. This combined quantity is called the Impedance of Element for Alternating Current. Impedance (Z)
=
E
I Reactance : The Impedance of AC circuit contains two parts. One in which potential difference and current always remains in same phase and the other in which there is a phase difference of /2 (+ or -) b/w potential difference and current. This second part is called Reactance (X). So, Q.5
Z
=
R
0
+
X
±
/2
Determine the Impedance of L-R Circuit and show that in such a Circuit Current lay behinds the Voltage.
Ans.: AC Circuit containing Inductance L and Resistance R in the Series : Consider a circuit in which Inductance L and Resistance R are connected in Series with source of alternating EMF E
=
E0Sinwt
(1)
Electrical Circuit and Circuit Analysis
63
Let I be the current in the circuit at any instant and VL and VR are the potential differences across L and R respectively at the instant, then And
VL
=
IXL
VR
=
IR
=
IωL
Now, VR is in phase with the current while VL leads the current by mutually perpendicular.
Vector Diagram of this Circuit
/2,
64
In this diagram vector OA represents VR (which is in phase with I) while OB represents VL (which leads I by 90˚). The vector OP represents the resultant of VR and VL, which is applied EMF (E), thus E2
=>
I
=
VR2 + VL2
=
(IR)2 + (IXL)2 E = VR2 + VL2 + 2VRVL2Cosθ
=
I2(R2 + XL2)
=
E R 2 + X L2
Here R2 + XL2
->
Effective resistance of L-R Circuit
This is called Inductive Impedance and given as ZRL. So,
ZRL
=
[ R2 + XL2 ]1/2
=
[ R2 + (ωL)2 ]1/2
If phase difference between voltage E and Resultant Current I is , then from vector diagram tan =
=
VL
=
IωL
=
ωL
VR
=
IR
=
R
tan-1 (ωL/R)
This is the angle by which the current lag behinds the voltage. Q.6
Determine the Impedance of R-C Circuit.
Ans.: AC Circuit containing Capacitance C and Resistance R in Series : Consider a circuit in which Capacitance C and Resistance R is connected in Series with the source of alternating EMF E
=
E0Sinwt
Electrical Circuit and Circuit Analysis
65
If I is the current in the circuit at any time t, then potential difference across R is VR = IR and across C is VC = IXC = I (1 / ωC) VR and I will be in same phase while VC will lag behind I by
/2 i.e. 90˚.
In this phase diagram, VR is represented by OA and VC by OB. The vector OP represents the resultant of VR and VC, which is applied Emf E.
66
E2
=>
I
=
VR2 + VL2
=
(IR)2 + (IXC)2
=
I2(R2 + XC2)
=
E R2 + XC2
Here R2 + XC2
->
Effective resistance of R-C Circuit
This is called Capacitive Impedance and given as ZRc. So, Q.7
ZRC
=
R2 + XC2
=
R2 + (1/ωC)2
What is meant by Resonance in LCR Circuit. Determine Resonant Frequency.
Ans.: If an AC circuit contains Inductance (L), Capacitance (C) and Resistance (R) in Series, then Impedance (Z) of this series combination is obtained as – (IZ)2 =
(IR)2 + (IXL – IXC)2 {E2 = VR2 + (VL – VC)2} {E = IZ; VL = IXL; VR = IR; VC = IXC}
OR
Z2
=
R2 + (XL –XC)2
=>
Z
=
[R2 + (XL –XC)2 ]1/2
By putting the value of XL and XC Z
=
[R2 + (ωL –1/ωC)2 ]1/2
From this equation, we see that when frequency increases, Inductive Reactance ωL and Capacitive Reactance 1/WC decreases, its opposite takes place. Therefore by adjusting frequency or values of reactive components, a condition (ωL = 1/ωC) can be achieved, so that resultant reactance (ωL – 1/ωC) becomes zero. At this frequency the Impedance of the Circuit becomes minimum equal to Resistance R and current in the circuit is maximum. This state of circuit is called Electrical Resonance. The frequency at which Resonance take place, is called Resonant Frequency. At Resonant Frequency, current and voltage are in phase. At Resonant Frequency (ω = ω0)
Electrical Circuit and Circuit Analysis
67
XL
=
XC
=>
ω0L
=
1/ω0C
=>
ω02
=
1/LC
=>
2 F0 =
1 LC
=>
F0
=
1 2
Hertz
LC
In Resonance State (At Resonant Frequency) :
Q.8
(1)
Z
=
ZMin
=
R
(2)
Current in the circuit is maximum IMax = E/R
(3)
Resultant Reactance of circuit becomes zero.
Obtain the expression for Power Consumed in an AC Circuit and define Power Factor.
Ans.: Power in AC Circuit and Power Factor : In an AC circuit voltage and current have a phase difference therefore power in AC circuit also depends on this phase difference. Suppose at time t alternating EMF and current in AC Circuit are and
E
=
E0Sinwt
I
=
I0Sin(wt - )
The instantaneous power in the circuit at time t will be Pi
=
E0Sinwt
X
I0Sin(wt - )
=
E0 I0 Sinwt Sin(wt - )
=
1/2 [Cos(C – D) – Cos(C + D)]
Since, SinC SinD So,
Pi
= 1/2 E0 I0 [Cos{wt – (wt - )} – Cos{wt + (wt - )}]
68
OR
Pi
= 1/2 E0 I0 [Cos – Cos(2wt - )] = 1/2 E0 I0 Cos – ½ E0 I0 Cos(2wt - )
First part of instantaneous power does not depend on time and second part changes periodically with time. For the periodic variation, the average value of ½ E0 I0 Cos(2wt - ) is zero. So,
Pav
Pav
=
½ E0 I0 Cos
=
E0
I0 Cos
2
2
=
Erms Irms Cos
Here Cos is called Power Factor i.e. in an AC circuit, the cosine of phase difference between the voltage and current i.e. Cos is called Power Factor. Q.98 Define Half Power Frequency and Band Width. Ans.: Half Power Frequencies and Band Width of a Series Resonant Circuit : The Resultant Impedance of Series LCR Circuit is Z
=
[R2 + (ωL –1/ωC)2 ]1/2
Electrical Circuit and Circuit Analysis
69
In the state of Resonance, when ωL = 1/ωC., Z = R and current will be in phase with applied EMF. At Resonant Frequency, current in the circuit will be maximum. As shown in figure at Resonant Frequency (F0), current is maximum and at Frequencies F1 and F2, current in the circuit is 1/ 2 times, the Maximum Current (IMax). The Power at these Frequencies F1 and F2 is half the Power at Resonant Frequency because
Power
I2
These Frequencies F1 and F2 are therefore called Half Power Frequencies and corresponding points on the Resonance Curve are called Half Power Points. Band Width : The Frequency Interval (F2 – F1) between which the circuit becomes capable of accepting more power from the source is called Band Width of the circuit. Thus Band Width ∆F
=
F2 – F1
Q.10 Explain Star and Delta Connections of Three Phase AC Circuit. Ans.: Star Connection : In this connection all the low potential points (starting points) are connected together and it is called Neutral P-terminal. The electrical power is terminated by three terminals, which are high potential terminals (finish ends).
70
The voltage between any pair (1-2, 2-3, 3-1) is called Line Voltage and is 3 times the voltage generated in one armature windings. However the line current is equal to phase current. For domestic purpose, a single phase AC is provided i.e. load connection is made between a line (1, 2 or 3) and the neutral (4) for running heavy machinery three phase AC provided i.e. load is connected between 1 and 2 or 2 and 3 or 3 and 1. Delta Connection : In this connection, low potential point of one phase winding is connected to high potential point of second phase winding and so on. There is no neutral in Delta Connection i.e. to transmit required amount of power only, three conducting wires are required in delta connection. In this connection, line voltage is equal to phase voltage, however the line current is 3 times the phase current.
Multiple Choice Questions Q:1
In a series resonant circuit, the current at resonance is: (a) maximum (b) minimum (c) zero (d) none of the above
( )
Electrical Circuit and Circuit Analysis
2
3
4
The resonant frequency of a circuit is given by: (a)
(b)
(c)
(d)
6
7
9
(d)
In an deal circuit, the power is consumed in: (a) R (b) (c) L (d)
( )
Zero
( )
C L and C
( )
None of the above
( )
The impedance of an R- L series circuit is given by: (a)
R + XL
(b)
(c)
R2 +
(d)
In LCR circuit, the power factor to be 1, the condition is: (a) R=O (b) (c)
8
( )
Resonant circuits are: (a) Parallel resonant circuits (b) Series resonant circuits (c) Both parallel and series resonant circuits (d) None of the above The average value of alternating current over one complete cycle is: (a) Io (b) (c)
5
71
(d)
When frequency of an parallel LCR circuit increase, the impedance Z: (a) First decreases and then increase (b) First increase and then decreases (c) Increases uniformly (d) Decreases uniformly When two parallel wires carry current in the same direction, they:
( )
72
(a) (b) (c) (d) 10
11
12.
13
14
15
16
17
Repel each other Attract each other Have no force between them Apply an uncertain force on each other
( )
If direct current is passed in a spring, then: (a) Its length decreases (b) Its length increases (c) No change occurs in the length (d) It oscillates The unit of magnetic flux density is: (a) weber/m (c) weber/m2
( )
(b) (d)
weber ampere/m
( )
Lenz's law is based on the conservation of: (a) Charge (b) (c) Energy (d)
Momentum Mass
( )
The time constant of an L -R circuit is: (a) LR (c) R/L
L/R I/RL
( )
Permeability of a material is: (a)
(b)
(c)
(d)
(b) (d)
( )
Copper is: (a) Paramagnetic (c) Diamagnetic
(b) (d)
Ferromagnetic Non-magnetic
( )
The example of ferromagnetic material is: (a) Aluminum (c) Mercury
(b) (d)
Nickel Manganese
( )
In an a.c. circuit the peak values of current and e.m.f compared to the values measured by a.c. instruments are: (a) 1.41 times (b) 0.707 times (c) Double (d) Half ( )
Electrical Circuit and Circuit Analysis
73
18
The voltage of domestic power supply is 220 volts. What does this voltage represent? (a) Mean voltage (b) Mean-square voltage (c) Root-mean square voltage (d) Peak voltage ( )
19
A generator is based on the principle of: (a) Self inductance (c) Electromagnetic induction
20.
21.
22
23
24
25
(b) (d)
Electrical induction Mutual induction
The impedance of a 200 mH induction coil at 1 KHz will be: (a) 200 ohms (b) 1257 ohms (c) 628 ohms (d) 12.57 x10 5 The unit of is: (a) Henry (b) (c) Ampere (d) The time constant of an L R circuit is given by: (a) R/L (b) (c) RL (d)
( )
( )
Farad Second
( )
L/R R2 L
( )
In a pure capacitor: (a) current leads the e.m.f. by phase 90o (b) current legs behind the e.m.f. by phase 90o (c) current of e.m.f. are always in the same phase (d) current and e.m.f. are always opposite phase
( )
In an ideal A.C. circuit the power is consumed in: (a) Resistance (b) Capacitance (c) Inductance (d) L C Circuit
( )
The resonant frequency of series LCR circuit consists of R = 100 mH is: (a) 10 Hz (c) 500 Hz
(b) (d)
100Hz 5000 Hz
and L= 100
( )
74
S.NO. Ans S.NO. Ans S.NO. Ans
1 A 10 C 19 C
2 A 11 C 20 B
3 C 12 C 21 D
4 D 13 B 22 B
5 D 14 C 23 B
6 B 15 C 24 D
7 C 16 B 25
8 B 17 A
9 A 18 C
Electrical Circuit and Circuit Analysis
75
Chapter-6
Electrical Devices, Machines And Measuring Instruments Q.1
Describe construction and working of DC Motor. Give expression for its efficiency.
Ans.: DC Motor : It is a machine which converts electrical energy into mechanical energy. Construction : It consists of following five parts : (i)
Armature : The armature coil consists of a large no. of turns of insulated copper wire wound over a soft iron core.
(ii)
Filed Magnet
(iii)
Split Rings or Commutator : These are two halves of same ring, the ends of armature coil are connected to these halves which also rotate with armature.
(iv)
Brushes : These are two carbon rods and connected to an external source of DC supply.
(v)
Battery
Working : As key (K) is closed, current lows in armature coil. Due to this arms AB and CD experience equal and opposite force (according to Fleming‟s Left Hand Rule). These forces constitute a couple and Torque due to this couple is
=
niBASinθ
76
n ->
No. of turns in armature
I ->
Current through the coil
B ->
Intensity of Magnetic Field
A ->
Area of the coil
θ ->
Angle which the normal to the area makes with Magnetic Field.
This Torque tries to bring plane of coil perpendicular to magnetic field thus θ = 0, Sinθ = 0 and So,
=
0
After every half rotation, direction of current in coil is reverted by commutator and Torque acting on coil remains in same direction. Thus, the coil goes on rotating till the supply of current is maintained with this coil. The shaft rotates and shaft can be connected to any machine for its operation.
Efficiency of Electric Motor :
Electrical Circuit and Circuit Analysis
Efficiency ŋ =
77
Work done by Motor per second
X 100%
Energy supplied by external source per second =>
ŋ
=
W
X
100%
X
100%
X
100%
P =>
ŋ
=
Ie IE
=>
ŋ
=
e E
Where E -> Applied EMF by Source E -> Induced Back EMF Q.2
Explain the principles and working of a Transformer. What is Transformer Ratio?
Ans.: Transformer : It is an electrical device which is used for changing the AC voltage. It is based on the principle of mutual induction.
Working : When alternating current is passed through the primary coil, a Magnetic Field is produced. Due to continuous change in alternating current in primary coil, the Magnetic Flux linked with secondary also changes, resulting the
78
generation of induced EMF in the secondary. This induced EMF depends on the ratio of no. of turns in the secondary to the no. of turns in primary. Let,
np -> No. to turns in primary coil ns -> No. of turns in secondary coil
Assuming there is no flux leakage and area of cross section in the same. Let flux passing through primary and secondary is . Then flux linked with primary coil p
=
- np d
(1)
dt s
=
- ns
d
(2)
dt Es Ep
=
ns
=
K
(3)
np
From this equation (3), we see that ratio of alternating EMF obtained in secondary to alternating EMF applied in the Primary is equal to ratio of no. of turns in secondary coil to no. of turns in Primary Coil. This ratio K is called Transformer Ratio.
Q.3
How is a Moving Coil Galvanometer modified to work as an Ammeter and a Voltmeter?
Ans.: Conversion of Galvanometer into Ammeter and Voltmeter : Ammeter : Ammeter is used for measuring the strength of current in electric circuit. It is always connected in series in the circuit. Resistance of ideal ammeter is zero. If a low resistance wire (shunt) of proper value is connected in parallel with the moving coil galvanometer, it is converted into ammeter.
Electrical Circuit and Circuit Analysis
79
I
ig G
I - ig VVVVVV S Converted Ammeter If G is resistance of galvanometer ig is the full scale deflection current of galvanometer. To convert a galvanometer into ammeter of Range I, a shunt of resistance S is connected in parallel with the galvanometer. From the circuit diagram (I – ig) S
=
ig G
S
=
ig
G
(I - ig) Voltmeter : It is used for measuring potential difference between any two points in a circuit. If a proper value of high resistance is connected in series with the coil of moving coil galvanometer, then it is converted into voltmeter.
R G
VVVVVV
Converted Voltmeter Suppose the resistance of galvanometer which is to be converted into voltmeter is G and full scale deflection current is ig, if the galvanometer is to be converted into a voltmeter of range V volt, then a high resistance R is connected in series with
80
coil so that ig should flow through the resistance (R + G) on applying a potential difference V i.e. V
=
R
=
ig (R + G) V
- G
ig Q.4
What is a Multimeter? Discuss the design of a Multi Range Voltmeter.
Ans.: Multimeter : It is an electronic instrument which can measure currents, voltages and resistances. Using Function Switch and Range Switch, it can be used as voltmeter, ammeter or ohmmeter for different ranges of measurement. A multimeter consists of an ordinary pivoted type of moving coil galvanometer. Voltage Measurement : For mMeasurement of voltage, A Resistance Rs is connected in series with the coil, so that when maximum voltage is applied, the current through the movement is ig. Assuming,
ig
=
1 mA
Coil Resistance
Rs
=
500 Ω
For a Range of 10V, Rs will be ig (G + Rs) Rs
= =
V
= 10
1 X 10-3 Similarly for 100V, Voltage Range Rs = 999.5 K Ω.
10V -
500
= 99.5 K Ω
Electrical Circuit and Circuit Analysis
81
So, by using different series resistors the range of voltage measurement can be increased.
Multiple Choice Questions 1
2
3
The function of d.c. motor is: (a) to convert energy to electrical energy (b) to convert electrical energy to mechanical energy (c) to convert electrical energy to magnetic energy (d) to convert magnetic energy of electrical energy The efficiency of a .d. c motor is: (a)
(b)
(c)
(d)
None of the above
To convert mechanical energy into electrical energy, we can use:
( )
( )
82
(a) (c) 4
5
6
7
8
9.
10.
11
Dynamo Transformer
Transformer is based on the principle of: (a) Self induction (c) Electromagnetic
(b) (d)
Motor Galvanometer
( )
(b) (d)
Mutual induction Electrical induction
( )
A galvanometer can be changed into ammeter by: (a) Adding a low resistance in series with it (b) Adding a low resistances in parallel with it (c) Adding a high resistance in series with it (d) Adding a high resistance in parallel with it For an ideal voltmeter, the resistance should be: (a) Zero (b) (c) Very high (d) An active element in a circuit is one which: (a) Receives energy (c) Both (a) and (d) 2 Wb/m equals: (a) 1 Gauss (c) 103 Gauss
( )
Infinite None of the above
( )
(b) (d)
Supplies energy None of the above
( )
(b) (d)
102 Gauss 104 Gauss
( )
The heating of the large transformers is due to: (a) the heat generated by current (b) hysteresis alone (c) both the hysteresis and heating effect of current (d) none of the above
( )
Lenz's law is a consequence of the law of conservation of: (a) charge (b) mass (c) momentum (d) energy
( )
The back e.m.f. in d.c. motor is maximum when: (a) the motor has picked up maximum speed (b) the motor has just started moving (c) the speed of the motor is till on the increase (d) the motor has just been switched off
( )
Electrical Circuit and Circuit Analysis
12
13
14
15
16
17
18
83
A 100 mH coil carries a current of I A. energy stored in its magnetic field is: (a) 1J (b) 0.5 J (c) 0.05 J (d) 0.1 J
( )
Eddy currents are produced when: (a) a metal is kept in a varying magnetic field (b) a metal is kept in a steady magnetic field (c) a circular coil is placed in a magnetic field (d) a current is passed through a circular coil
( )
Lamination of transformer core: (a) eliminates heating due to eddy current (b) eliminates magnetic field due to eddy current (c) eliminates both heating and magnetic field due to eddy current (d) none of the above
( )
In a transformer Vp = 220 V and Vs = 22 v. it runs a machine of 220 resistance. The current in the primary coil is: (a) 1A (b) 0.1 A (c) 0.01 A (d) 1mA ( ) The current between two infinite straight conductors separated by a distance 10 m are 2 A and 4 A respectively. The force per unit length between them is: (a) 1.8 X 10–3 N/m attractive (b)
1.6 X 10–3 N/m repulsive
(c)
3.2 X 10–3 N/m attractive
(d)
3.2 X 10–3 N/m repulsive
( )
According to faraday's law of e.m. finduction the inducted e.m.f. 'e' is: (a)
(b)
(c)
(d)
In the given resistor circuit, the current flowing through the resistance CD will be:
( )
84
(a) (b) (c)
4
C 2
D
I
4 10 V
(d) 19
20
21
22
23
24
25
A multi meter cannot be used to measure: (a) current (c) resistance A generator is based on the principle of: (a) Salf-inductance (c) Electromagnetic induction
(b) (d)
voltage capacitance
( )
(b) (d)
Electrical induction Mutual induction
( )
The back e.m.f. in d.c. motor is maximum when: (a) the motor has picked up maximum speed (b) the motor has just started moving (c) the speed of the motor is till on the increase (d) the motor has just been switched off
( )
A 100 mH coil carries a current of I A. energy stored in its magnetic field is: (a) 1J (b) 0.5 J (c) 0.05 J (d) 0.1 J
( )
Eddy currents are produced when: (a) a metal is kept in a varying magnetic field (b) a metal is kept in a steady magnetic field (c) a circular coil is placed in a magnetic coil (d) a current is passed through a circular coil
( )
Lamination of transformer core: (a) eliminates heating due to eddy current (b) eliminates magnetic field due to eddy current (c) eliminates both heating and magnetic field due to eddy current (d) none of the above
( )
Ina transformer Vp = 220 V and Vs = 22 v. it runs a machine of 220 current in the primary coil is: (a) 1A (b) 0.1 A (c) 0.01 A (d) 1mA
resistance. The
( )
Electrical Circuit and Circuit Analysis
26
27
S.NO. Ans S.NO. Ans S.NO. Ans
85
In LCR parallel circuit: (a) I is minimum, Z is minimum (b) I is minimum, z is maximum (c) I is maximum, Z is minimum (d) I is maximum, Z is maximum
( )
In comparison to d.c. transmission losses in a.c. are: (a) high (b) low (c) negligible (d) none of the above
( )
Q:1 B 10 D 19 D
2 D 11 A 20 C
3 A 12 B 21 A
4 B 13 C 22 B
5 A 14 C 23 C
6 A 15 B 24 C
7 C 16 B 25 B
8 D 17 A 26 B
9 C 18 C 27 B
86
Chapter-7
Electrical Wiring Q.1
What is Fuse? Discuss the Types of Fuses generally used.
Ans.: Fuse : It is a safety device used to prevent serious damage to an electrical installation due to fault in it. It is a small wire of tinned copper or an alloy (lead + tin) having a low melting point. It is connected in series with circuit. When a heavy current flows due to short circuit, the fuse melts or blows, cutting off further flow of current. In domestic installation, two types of fuses are used –
Q.2
(i)
Carbidge Type : It consists of a small tube of insulating material at glass having brass caps at its ends. The tube may be filled with non-ignitable powder. The fuse wire is held between the brass caps. The fuse wire is of such a gauge that when the current exceeds a specified value, the wire melts and circuit breaks.
(ii)
Re-wirable Type : This fuse has a Porcelain Fuse Holder with terminal clips between which the Fuse wire is fixed by screws. The fuse holder is gripped in spring contacts in a Porcelain base.
What is Earthing? Explain its importance.
Ans. Earthing of electrical appliances, power supply systems etc. is an essential gradient of electrical wiring. Majority of electrical accidents may be directly traced to inadequate, faulty or some times no earthing. When the insulation of the line conductor goes bad and the conductor comes into contact with the metal casing of an electrical appliance or a metallic conduits etc., the casing or conduit
Electrical Circuit and Circuit Analysis
87
would become live. There would be no outward indication for this defect. If a person touches the appliance while standing on the ground, current would pass to earth through his body and he would receive a severe shock which could be sometimes fatal. On the other hand if all metal casing, conduits etc. are connected to a good earth by a conductor, the casing will remain at the same potential as earth i.e. at zero potential. Further the earth connection provides an easy path (of low resistance) so when a fault occurs large current will flow which will „blow‟ the fuses and power supply will be cut off. Hence the metal casing of all appliances, distribution boards and earthing pins of 3-pin plugs must be connected to a proper earthing. Q.3
Discuss the various Types of Wiring used in a household installation.
Ans.: There are number of types of wiring used for domestic installations. These are – (i)
Casing and Copping : In this wiring, a teak wood casing having grooves length wise is used. The wires vulcanized rubber insulated (VIR) or plastic insulated are placed in these grooves, the casing is covered by a thin strip of teak wood and fixed by screws.
(ii)
Cleat Wiring : In this method, the wires are stretched and gripped between two halves of Porcelain cleats fixed to the walls.
(iii)
Tough Rubber Sheathed (TRS) and Cab Tyre Sheathed (CTS) wiring : The TRS cables consists of conductors which after being insulated are sheathed in a layer of tough rubber which provides a good degree of protection against moisture.
(iv)
Lead Sheathed Wiring : The lead covered cables have a long life and medium cost and provide a good protection against moisture but are not very strong mechanically.
(v)
Metal Conduit Wiring : In this system the insulated cables are drawn in metallic conduits which are initially installed in desired positions. It has very long life.
Objective Part: Multiple Choice Questions: Q:1
A fuse wire has: (a) a low melting point (b) a low resistance (c) a small radium
88
2
3
4
S.NO. Ans
(d) negligible mechanical strength Single-phase domestic power supply is at: (a) 400 V, 50 Hz (c) 220 V, 100 Hz A switch can : (a) open a circuit (c) both open and close a circuit Earthing is used: (a) As a neutral line (c) to reduce voltage fluctuation
Q:1 A
2 C
3 C
4 D
( )
5
(b) (d)
220 V. 50 Hz 400 V, 100 Hz
( )
(b) (d)
close a circuit introduce a resistance
( )
(b) (d)
to save power as a safety measure
( )
Electrical Circuit and Circuit Analysis
89
Chapter-8
Network Analysis Q.1
State Thevenin’s Theorem.
Ans.: Thevenin’s Theoram : According to this theorem, “Any two terminal linear network containing voltage sources and impedances can be replaced with an equivalent voltage source Eeq with a series impedance Zeq. The values of Eeq is the open circuit voltage between the given terminal of the network and Z eq is the impedance across these terminals when all the generators in the network have been replaced by their internal impedances.”
Consider a Simple Circuit :
90
The total impedance across the voltage source is Z =
Z1
+
Z3 (Z2 + ZL) Z2 + Z 3 + Z L
=>
Z
=
Z1 Z2 + Z2 Z3 + Z3 Z1 + ZL (Z1 + Z3) Z3 + Z2 + ZL
So,
I =
E
=
E
Z Thus,
IL =
Z3 + Z 2 + Z L Z1 Z2 + Z2 Z3 + Z3 Z1 + ZL (Z1 + Z3)
Z3
I
Z3 + Z 2 + Z L => =>
IL =
Z3
Z3 + Z 2 + Z L
Z3 + Z 2 + Z L
Z1 Z2 + Z2 Z3 + Z3 Z1 + ZL (Z1 + Z3)
IL =
Z3
E
E
Z1 Z2 + Z2 Z3 + Z3 Z1 + ZL (Z1 + Z3)
(1)
Now the open circuit voltage across A, B is voltage across P, Q when Z L is disconnected. Eeq
=
E
Z3
Z1 + Z 3 The impedance across A, B in this condition is Zeq
=
Z1
+
Z3 Z1 Z3 + Z 1
=>
Zeq
=
Z1 Z2 + Z2 Z3 + Z3 Z1 Z1 + Z 3
So, using the equivalent circuit, the current in the load will be IL
=
Eeq Zeq + ZL
=>
IL
=
Z3 Z1 + Z 3
Z1 + Z 3 Z1 Z2 + Z2 Z3 + Z3 Z1 + ZL (Z1 + Z3)
E
Electrical Circuit and Circuit Analysis
=>
IL
=
91
Z3 Z1 Z2 + Z2 Z3 + Z3 Z1 + ZL (Z1 + Z3)
E (2)
Which is same as given by equation (1), verifying Thevenin‟s Theorem. Q.2
State Norton’s Theorem and explain application for complicated network.
Ans.: Norton’s Theorem : According to this theorem, “Any complicated linear two terminal network can be replaced by an equivalent circuit consisting of a constant current generator, Ieq, with an impedance Zeq connected parallel to it. The current generated Ieq is equal to the short-circuit current between the given terminals and the parallel impedance Zeq is the open circuit impedance between these terminals with all sources of emf replaced by their internal impedances.”
This Theorem can easily be proved by first obtaining the Thevenin‟s equivalent circuit. Accordingly,
92
(IL)T
=
Eeq Zeq + ZL
If now the terminals A, B are short circuited the short-circuit current Ieq
=
Eeq Zeq
Using this value of current in the Norton‟s equivalent circuit, the current I L in the load by division of current in parallel branches will be (IL)N
=
Zeq
Ieq
Zeq + ZL =>
(IL)N
=
Zeq
Eeq
Zeq + ZL Zeq =>
(IL)N =
Eeq Zeq + ZL
Thus the current in the load (IL)N obtained by Nortan‟s equivalent circuit is same as the current (IL)T obtained by Thevenin‟s circuit. Q.3
Give Maximum Power Transfer Theoram.
Ans.: Maximum Power Transfer Theorem : According to this theorem, “The transfer of power from a generator to a load will be maximum when the load impedance is the complex conjugate of the internal impedance of the generator.” Thus, if internal impedance of generator is RG + XG ± /2 i.e., having a resistance part RG and reactive part XG, the transfer of power to a load will be maximum when the load impedance has a resistive part RL equal to RG and a reactive part XL equal in magnitude to XG but opposite in nature. Hence if generator reactance is capacitive, the load impedance must be inductive. For dc circuits the reactive part has no role, so according to the maximum power transfer theorem, “the transfer of power to a load is maximum when the load resistance is equal to the internal impedance of the generator.”
Electrical Circuit and Circuit Analysis
93
To establish this theorem, consider a dc circuit with a generator of emf E and internal resistance RG. It is connected to a load RL. The current in the circuit will be I
=
E RL + R G
So, power delivered to the load is PL PL
=
I 2 RL
=
E2 RL (RL + RG) 2 E2RL
=
(RL2 + RG 2 + 2 RL RG) PL
=
E2RL (RL - RG) 2 + 4 RL RG
PL will be maximum when denominator in the above expression is minimum. So for maximum power RL and
(PL)Max
= =
RG
E2RL 4 RL RG
=
E2 4 RG
=
E2 4 RL
94
Multiple Choice Questions: Q:1 Norton theorem is converse of: (a) The venin's theorem (b) Superposition theorem (b) Reciprocity theorem (d) Maximum power transfer theorem 2
A four terminal network has: (a) Two ports (c) Three ports
S.NO. Ans
1 A
( )
(b) (d)
One port No port
2 A
( )
Electrical Circuit and Circuit Analysis
95
BACHELOR OF COMPUTER APPLICATIONS (Part-I) EXAMINATION (Faculty of Science) (Three – Year Scheme of 10+2+3 Pattern) PAPER - 111
ELECTRICAL CIRCUIT AND CIRCUIT ANALYSIS OBJECTIVE PART- I Year - 2011 Time allowed : One Hour Maximum Marks : 20 The question paper contains 40 multiple choice questions with four choices and student will have to pick the correct one (each carrying ½ mark). 1.
The force of attraction or repulsion between charges follows: (a) Square law of distance (b) Inverse square law of distance (c) Both (a) and (b) (d) None of (a) and (b) ( )
2.
When the distance between two equal charges is decreased to half and their magnitude of charges also decreased to half, the force between them: (a) Remains unchanged (b) Reduces to half (c) Becomes half (d) None of the above ( )
3.
Electric field intensity due to a point charge follows: (a) Falls inversely proportional to the distance (b) Falls inversely proportional to the square root of the distance (c) It does not change with distance (d) Falls inversely proportional to the square of the distance
( )
One volt potential difference is equivalent to: (a) 1 Newton/coulomb (b) (c) 1 Joule/coulomb (d)
1 erg/Coulomb 1 Coulomb/Joule
( )
In a charged capacitor, the energy appears as: (a) Magnetic energy (b) (c) Electrostatic energy (d)
Electromagnetic energy Mechanical energy
( )
4.
5.
96
6.
7.
8.
Unit of capacitance is: (a) Coulomb (c) Henry
(b) (d)
Volt Farad
( )
What is the potential due to a point charge ‘q’ at a distance ‘r’ from it: (a)
(b)
(c)
(d)
( )
Energy stores in an electric field is given by: (a)
(b)
(c)
(d)
( )
9.
Three resistance of 500 ohm, 5000 0hm and 50 ohm are connected in series across a 555 volt main. What is the current flowing through them? (a) 1A (b) 100 mA (c) 10 mA (d) 10 A ( )
10.
If two capacitances of 100 f and 150 f are connected in parallel, what will be their total capacitance? (a) 60 f (b) 250 f (c) 15 f (d) None of the above ( )
11.
Capacitive time constant is given by: (a) (c)
12.
RC
(b) (d)
The energy stores in a magnetic field is given by:
( )
Electrical Circuit and Circuit Analysis
97
(a)
(b)
(c)
(d)
LI2
( )
13.
Two resistances of 0.275 ohm and 0.778 ohm are connected in parallel. The total resistance shall be: (a) More than 0.275 ohm (b) Less than 0.275 ohm (c) Equal to 1.053 ohm (d) More than 0.778 ohm ( )
14.
The ‘electron-volt’ is a unit of: (a) momentum (c) electric current
15.
16.
17.
18.
(b) (d)
potential difference energy of the electron
In a series resonant circuit, the current at resonance is: (a) maximum (b) minimum (c) zero (d) none of the above
( )
( )
The resonant frequency of a circuit is given by: (a)
(b)
(c)
(d)
( )
Resonant circuits are: (a) Parallel resonant circuits (b) Series resonant circuits (c) Both parallel and series resonant circuits (d) None of the above
( )
The effective capacitance is reduced when capacitor are connected in: (a) Series (b) Parallel (c) Series Parallel Combination (d) None of the above
( )
98
19.
20.
Ohm’s law does not apply to: (a) A.C. circuits (b) Conductors (c) Semi-conductor (d) Conductor when there is change in temperature
( )
The effective capacitance between ‘A’ and ‘B’ is:
2µf
2µf
A
B 2µf
(a)
1 f
(c) 21.
22.
(b) f
The resistivity of a wire depends on: (a) Its length (c) Both (a) and (b)
f
(d)
3 f
( )
(b) (d)
Its cross section On the material
( )
The resistant between A and B of the circuit given below: 3
3
B
A 3
(a) (c)
12 3
3
(b) (d)
6 1
( )
Electrical Circuit and Circuit Analysis
23.
24.
25.
26.
27.
28.
29.
30.
99
Magnetic induction due to a solenoid of length ‘L’ radius R, no. 7 turns N and current I is: (a) (b) (c)
(d)
The unit of magnetic flux density is: (a) Weber/m (c) Weber/m2
(b) (d)
The commercial unit of electrical energy is: (a) Joules (b) (c) Kilowatt (d)
( )
Weber amp/m
( )
Watt Kilowatt hour
( )
The function of d.c. motor is: (a) to convert energy to electrical energy (b) to convert electrical energy to mechanical energy (c) to convert electrical energy to magnetic energy (d) to convert magnetic energy of electrical energy
( )
Lenz’s law is based on the conservation of: (a) Charge (b) (c) Energy (d)
( )
Momentum Mass
The permeability of a material is: (a)
(b)
(c)
(d)
Copper is: (a) Paramagnetic (c) Diamagnetic
(b) (d)
Ferromagnetic non-magnetic
( )
The example of ferromagnetic material is: (a) Aluminum (c) Mercury
(b) (d)
Nickel Manganese
( )
( )
100
31.
32.
33.
34.
35.
36.
37.
A generator is based on the principle of: (a) Salf-inductance (c) Electromagnetic induction
(b) (d)
Electrical induction Mutual induction
( )
The impedance of 200 mH induction coil at 1 KHz will be: (a) 200 ohms (b) 1257 ohms (c) 628 ohms (d) 12.57.105 ohms
( )
Norton theorem is converse of: (a) Thevenin’s theorem (b) Superposition theorem (c) Reciprocity theorem (d) Maximum power transfer theorem
( )
A four terminal network has: (a) Two ports (c) Three ports
(b) (d)
One port No port
( )
Transformer ratio is 10. It means that: (a)
NS = 10 NP
(b)
Ns =
(c)
VS =
(d)
IS = 10 IP
A fuse wire has: (a) a low melting point (b) a low resistance (c) a small radium (d) negligible mechanical strength
( )
( )
Maximum power which a generator of e.m.f E and internal impedance Rg can supply to a load is: (a)
(b)
(c)
(d)
( )
Electrical Circuit and Circuit Analysis
101
38.
A cell of internal resistance 2 is connected to a variable external resistance R. The power in the external resistance will be maximum when R is equal to: (a) Zero (b) 1 ohm (c) 2 ohms (d) 6 ohms ( )
39.
An electric field can deflect: (a) X-rays (c) particles
(b) (d)
Neutrons rays
( )
Earthing is used: (a) As a neutral line (c) to reduce voltage fluctuation
(b) (d)
to save power as a safety measure
( )
40.
Answer Key 1. ( ) 2. ( )
3. ( )
4. ( )
5. ( )
6. ( )
7. ( )
8. ( )
9. ( )
10. ( )
11. ( )
12. ( )
13. ( )
14. ( )
15. ( )
16. ( )
17. ( )
18. ( )
19. ( )
20. ( )
21. ( )
22. ( )
23. ( )
24. ( )
25. ( )
26. ( )
27. ( )
28. ( )
29. ( )
30. ( )
31. ( )
32. ( )
33. ( )
34. ( )
35. ( )
36. ( )
37. ( )
38. ( )
39. ( )
40. ( )
__________
102
DESCRIPTIVE PART - II Year 2011 Time allowed : 2 Hours Maximum Marks : 30 Attempt any four questions out of the six. All questions carry 7½ marks each.
Q.1
Q.2
(a)
What is Coulomb’s law? Define electric lines of force.
(b)
What is difference between electric potential and potential difference?
(c)
Calculate the capacitance of series and parallel combination of three capacitors.
(a)
What is a condenser? Explain its principle.
(b)
Explain the use of condenser in electronic circuits. What is the gang condenser?
(c)
State Ohm’s law and define resistance of a conductor. On what factors and how does the resistance of a conductor depend?
Q.3
(a)
State Kirchhoff’s laws and explain their application with the help of examples.
(b)
Explain the series and parallel combination of resistances.
(c)
What is time constant? Show graphically the dependence of charging and discharging process of time constant.
Q.4
(a)
State Biot-Savarts Law. Using this obtain expression for magnetic induction at a point on the axis of a current carrying coil.
(b)
Calculate the magnetic induction inside a solenoid of 50 cm long and number of twins per unit length is 100, the current flowing in solenoid is 10 amp.
Q.5
Write short notes on the following:
Electrical Circuit and Circuit Analysis
Q. 6
103
(a)
Series resonance L-C-R circuit.
(b)
DC Motor.
(a)
State and prove Thevenin’s theorem. Find Norton’s equivalent of the Thevenin’s equivalent circuit.
(d)
Write the statement of reciprocity and maximum power transfer theorem.
___________
104
ELECTRICAL CIRCUIT AND CIRCUIT ANALYSIS PAPER - 111 OBJECTIVE PART- I Year - 2010 Time allowed : One Hour Maximum Marks : 20 The question paper contains 40 multiple choice questions with four choices and student will have to pick the correct one (each carrying ½ mark). 1.
2.
3.
A kilowatt hour is a unit of : (a) Energy (c) Electric Charge
(b) (d)
Power Electric Current
( )
Dielectric constant is a : (a) Dimensionless Quantity (c) Conversion Quantity
(b) (d)
Universal Constant None of the above
( )
A charge Q is situated at the centre of a cube. the electric flux emerging out through its surface will be : Q (a) (b) 2 0
(c) 4.
6.
8
(d) 0
Q 6
( ) 0
If dielectric medium of constant K is filled between the plates of a capacitor, then its capacity increases: (b) times (b) k times (b)
5.
Q
K2 times
(d)
( )
The Unit of electric field intensity is: (a) Newton/meter (c) Newton/Coulomb
(b) (d)
Coulomb/Newton Joule/Newton
( )
The value of 1 electron volt is: (a) 1.6 X 10–19J (c) 3.2 X 10–19J
(b) (d)
1.6 X 1019J 1.6 X 10–20 J
( )
Electrical Circuit and Circuit Analysis
7.
8.
9.
10.
105
The energy stored in an capacitor is in the form of: (a) Kinetic energy (b) Potential energy (c) Magnetic energy (d) Elastic energy
( )
The capacitance of a capacitor does not depend upon: (a) Shape of plates (b) Size of Plates (c) Charge on plates (d) Separation between plates
( )
A 4 µ F capacitor is charged to 400 V. The energy stored in it will be: (a) 0.16 J (b) 0.32 J (c) 0.64 J (d) 1.28 J
( )
Four capacitor each of capacity 3 Farad are connected in series. The resultant capacity will be: (a) (b) (c)
(d)
( )
11.
A parallel plate capacitor is given a charge Q. If the area of plates is doubled, its capacity will be: (a) Halved (b) Doubled (c) Zero (d) Unchanged ( )
12.
The specific resistance of a wire depends upon: (a) Its length (b) (c) Its dimensions (d)
13.
14.
15.
Its cross-section area Its material
( )
When two resistances are connected in series, they have: (a) Same voltage (b) Same resistance (c) Same current (d) Different current
( )
Unit of resistivity is: (a) ohm/meter (c) ohm-meter
( )
Kirchhoff's first low is related to the law of: (a) Conservation of energy (b) Conservation of charge (c) Conservation of mass
(b) (d)
ohm/meter2 ohm-meter2
106
(d) 16.
17.
Conservation of angular momentum
The conductivity of superconductor is : (a) Infinite (c) Very small
( )
(b) (d)
Very large Zero
( )
The current i in the given circuit is:
2V
+ -
30
30
30
18.
(a)
(b)
(c)
(d)
The example of non-ohmic resistance is: (a) Copper wire (c) Diobe
(b) (d)
( )
Carbon wire Tungsten wire
( )
19.
The path of a charged particle moving in a direction perpendicular to the magnetic field is: (a) Elliptical (b) Rectangular (c) Circular (d) Helical ( )
20.
The magnetic induction at the centre of a circular current carrying coil of redius 'r" is: (a) µOni (b) 2µOni 2a a (c) µOni (d) Zero ( ) a
21.
The rays which remain unperfected in a magnetic field are: (a) (c)
(b) (d)
Positive rays
( )
Electrical Circuit and Circuit Analysis
22.
23.
The cause of diamagnetism is: (a) Orbital motion of electrons (c) Paired electrons
25.
(d)
28.
Zero
( )
( )
L=–
(c)
L=–
L=
(d)
( )
The peak value of a.c. is 4 Ampere the root mean square value of current in the circuit is: (a) 4 Ampere (b) Ampere Ampere
(d)
8 Ampere
( )
The average value of alternating current over one complete cycle is: (a) Io (b) (c)
27.
Spin motion of electrons None of the above
The coefficient of self induction of a coil is given by: e (b) L= (b)
(c) 26.
(b) (d)
A bar magnet of magnetic moment 'M' is cut into two equal parts. The magnetic moment of either of part will be: (a) 2M (b) (c)
24.
107
(d)
In an deal circuit, the power is consumed in: (a) R (b) (c) L (d)
Zero
( )
C L and C
( )
None of the above
( )
The impedance of an R- L series circuit is given by: (a)
R + XL
(b)
(c)
R2 +
(d)
108
29.
In LCR circuit, the power factor to be 1, the condition is: (a) R=O (b) (c)
30.
31.
32.
33.
34.
35.
36.
(d)
When frequency of an parallel LCR circuit increase, the impedance Z: (a) First decreases and then increase (b) First increase and then decreases (c) Increases uniformly (d) Decreases uniformly
( )
The efficiency of a .d. c motor is: (a)
(b)
(c)
(d)
None of the above
( )
To convert mechanical energy into electrical energy, we can use: (a) Dynamo (b) Motor (c) Transformer (d) Galvanometer
( )
Transformer is based on the principle of: (a) Self induction (c) Electromagnetic
( )
(b) (d)
Mutual induction Electrical induction
A galvanometer can be changed into ammeter by: (a) Adding a low resistance in series with it (b) Adding a low resistances in parallel with it (c) Adding a high resistance in series with it (d) Adding a high resistance in parallel with it
( )
For an ideal voltmeter, the resistance should be: (a) Zero (b) (c) Very high (d)
Infinite None of the above
( )
An active element in a circuit is one which: (a) Receives energy (b) (c) Both (a) and (d) (d)
Supplies energy None of the above
( )
Electrical Circuit and Circuit Analysis
37.
38.
39.
40.
109
The maximum power transferred to the load P-L is: (a)
(b)
(c)
(d)
Norton theorem is converse of: (a) The venin's theorem (b) Superposition theorem (b) Reciprocity theorem (d) Maximum power transfer theorem
( )
A four terminal network has: (a) Two ports (c) Three ports
(b) (d)
One port No port
The permeability of a material is: (a) µ
(b)
µ
(c)
(d)
µ
µ
( )
( )
Answer Key 1. (a) 2. (a)
3. (a)
4. (b)
5. (c)
6. (a)
7. (b)
8. (c)
9. (b)
10. (a)
11. (b)
12. (d)
13. (c)
14. (c)
15. (b)
16. (a)
17. (c)
18. (c)
19. (c)
20. (a)
21. (c)
22. (c)
23. (b)
24. (a)
25. (c)
26. (d)
27. (a)
28. (b)
29. (c)
30. (b)
31. (a)
32. (a)
33. (b)
34. (b)
35. (b)
36. (b)
37. (c)
38. (a)
39. (a)
40. (b)
________
110
DESCRIPTIVE PART - II Year 2010 Time allowed : 2 Hours Maximum Marks : 30 Attempt any four questions out of the six. All questions carry 7½ marks each.
Q.1
(a)
Define electric field intensity. Derive an expression for electric field due to a point charge.
Q.2
(b)
What do you mean by the quantization of charge ?
(c)
Find out the capacitance of series and parallel combination of three capacitors.
(a)
Derive an expression for the capacitance of a parallel plate capacitor.
(b)
State Ohm's law and define resistance of conductor.
(c)
An electric bulb of 484
supplies light when connected to 220 V supply.
Calculate electric power of bulb and current flowing through it.
Q.3
(a)
What is drift velocity? Write its relation with current.
(b)
Discuss the effect of rise in temperature on the electrical conductivity of (i) Semiconductor (ii) Insulator.
(c)
Calculate the equivalent resistance between A and B in the following circuit.
A
Q.4
(a)
Explain Biot-Svart's law with diagram.
B
Electrical Circuit and Circuit Analysis
(b)
111
A current is flowing through a long straight wire. Find out the expression for magnetic field
Q.5
(c)
State and explain Lenz's law.
(a)
Define Z-factor and bandwidth for a series resonance L-C-R circuit.
(b)
Draw parallel L-C-R resonant circuit. How is it differ from a series resonant L-CR circuit?
(c)
The equation of an a.c. current is given by i=4 sin period of current.
Q.6
(a)
Explain construction and working of a.b.c. motor.
(b)
State and prove Thevenin's theorem.
__________
. Find out the time
112
ELECTRICAL CIRCUIT AND CIRCUIT ANALYSIS PAPER - 111 OBJECTIVE PART- I Year - 2009 Time allowed : One Hour Maximum Marks : 20 The question paper contains 40 multiple choice questions with four choices and student will have to pick the correct one (each carrying ½ mark). 1.
2.
3.
Which of the following is not conserved: (a) Mass (c) Total energy
One volt potential difference is equivalent to: (a) Newton/Coulomb (b) (c) Joule/Coulomb (d)
+Ke/r
( )
Erg/Coulomb Coulomb/Joule
( )
(d)
+Ke2/r
( )
The distance between two charges q1 and q2 is r, and then the electric potential energy of this system will be: (a) (b) (c)
5.
Charge Momentum
What will be the potential energy of the proton-electron system in a hydrogen atom? r is the radius of the orbit of the electron: (a) – Ke/r (b) –Ke2/r (c)
4.
(b) (d)
(d)
( )
A charge q is placed at a distance of 10 cm from a charge of 8 X 10 –8 C. If the force between the two charges is 0.072 N, the value of q is: (a) 10–3 C (b) 10–5 C (c)
10–6 C
(d)
10–8 C
( )
Electrical Circuit and Circuit Analysis
6.
7.
8.
9.
A capacitor stores energy in the form of : (a) Electromagnetic field (c) Electric Field
11.
(b) (d)
Magnetic field None of the above
( )
The capacitances of two capacitors are C1 and C2 It ehy charged to the same potential, then the ratio of their charges will be: (a)
(b)
(c)
(d)
Unit of capacitance is: (a) Coulomb (c) Henry
(b) (d)
Two capacitors of capacitances 2 equivalent capacitance will be: (a) 6 F
F and 4
( )
Volt Farad
( )
F are connected in series. Their
(b)
2
F
(d)
8
F
The resistance of a conductor depends on: (a) Its length only (c) Its temperature
(b) (d)
Its cross - sectional area All of the above
( )
Unit of potential difference is: (a) Volt (c) Joule
(b) (d)
Ampere Coulomb
( )
(c) 10.
113
F
( )
12.
The diameters of two resistance wires of equal length and of the same material are in the ratio of 1 : 2 the ratio of their resistances will be: (a) 1:2 (b) 1:4 (c) 4:1 (d) 2:1 ( )
13.
The conductivity of a superconductor is: (a) Zero (c) Large
14.
Unit of resistivity is :
(b) (d)
Small Infinite
( )
114
(a) (c) 15.
16.
ohm/m ohm=m
(b) (d)
ohm/m2 ohm-m2
In a closed circuit, kirchhoff's second law represents: (a) ohm's law (b) Charge - conservation law (c) Current-conservation low (d) None of the above
( )
( )
The charging current in R-C circuit varies with time I as: (a)
I = Ioe
(b)
I = Ioe
(c)
I = Io 1 - e
(d)
I = Io 1 + e
( )
17.
A bar magnet of magnetic moment M is cut into two equal pieces, perpendicular to its length. The magnetic of each piece will be: (a) M (b) M/2 (c) M/4 (d) 2M ( )
18.
When two parallel wires carry current in the same direction, they: (a) Repel each other (b) Attract each other (c) Have no force between them (d) Apply an uncertain force on each other
( )
If direct current is passed in a spring, then: (a) Its length decreases (b) Its length increases (c) No change occurs in the length (d) It oscillates
( )
19.
20
21.
The unit of magnetic flux density is: (a) weber/m (c) weber/m2
(b) (d)
Lenz's law is based on the conservation of: (a) Charge (b) (c) Energy (d)
weber ampere/m
( )
Momentum Mass
( )
Electrical Circuit and Circuit Analysis
22.
23.
24.
25.
115
The time constant of an L -R circuit is: (a) LR (c) R/L Permeability of a material is: (a)
(b)
(c)
(d)
(b) (d)
L/R I/RL
( )
( )
Copper is: (a) Paramagnetic (c) Diamagnetic
(b) (d)
Ferromagnetic Non-magnetic
( )
The example of ferromagnetic material is: (a) Aluminum (c) Mercury
(b) (d)
Nickel Manganese
( )
26.
In an a.c. circuit the peak values of current and e.m.f compared to the values measured by a.c. instruments are: (a) 1.41 times (b) 0.707 times (c) Double (d) Half ( )
27.
The voltage of domestic power supply is 220 volts. What does this voltage represent? (a) Mean voltage (b) Mean-square voltage (c) Root-mean square voltage (d) Peak voltage ( )
28.
A generator is based on the principle of: (a) Self inductance (c) Electromagnetic induction
29.
30.
(b) (d)
Electrical induction Mutual induction
( )
The impedance of a 200 mH induction coil at 1 KHz will be: (a) 200 ohms (b) 1257 ohms (c) 628 ohms (d) 12.57 x10 5
( )
The unit of is: (a) Henry (c) Ampere
( )
(b) (d)
Farad Second
116
31.
A choke coil has a high inductance and negligible resistance. Its power factor will be about: (a) 1.0 (b) 0.7 (c) 0.5 (d) Zero ( )
32.
A d.c. generator is based on the principle of: (a) Self inductance (b) (c) Electromagnetic induction (d)
Electrical induction Mutual induction
( )
The efficiency of an electric motor is: (a) E/e (c) e/E
(b) (d)
Ee/Ra E–e/Ra
( )
Transformer ratio is 10, means that: (a) Ns = 10 Np
(b)
Ns = Np/10
(c)
(d)
Is=10 Ip
33.
34.
35.
36.
37.
38.
Vs = Vp/10
( )
Series type most commonly used ohm meter is basically: (a) An ammeter (b) A voltmeter (c) Both ammeter as well as voltmeter (d) Neither ammeter nor voltmeter
( )
A fuse wire has: (a) A low melting point (b) A low resistance (c) A small radius (d) Negligible mechanical strength
( )
Maximum power which a generator of e.m.f. E and internal impedance Rg can supply to a load is: (a)
(b)
(c)
(d)
( )
A cell of internal resistance 2 is connected to a variable external resistance R The power in the external resistance will be maximum when R is equal to: (a) Zero (b) 1 ohm
Electrical Circuit and Circuit Analysis
(c) 39.
40.
117
2 ohms
(d)
4 ohms
( )
An electric field can deflect: (a) X-ray (c)
(b) (d)
Neutrons
Single-phase domestic power supply is at: (a) 400 V, 50 Hz (c) 220 V, 100 Hz
(b) (d)
220 V. 50 Hz 400 V, 100 Hz
( )
( )
Answer Key 1. (a) 2. (c)
3. (b)
4. (b)
5. (b)
6. (c)
7. (d)
8. (d)
9. (b)
10. (d)
11. (a)
12. (c)
13. (d)
14. (c)
15. (d)
16. (b)
17. (b)
18. (b)
19. (a)
20. (c)
21. (c)
22. (b)
23. (c)
24. (c)
25. (b)
26. (a))
27. (c)
28. (c)
29. (b)
30. (d)
31. (d)
32. (c)
33. (c)
34. (a)
35. (a)
36. (a)
37. (c)
38. (c)
39. (c)
40. (b)
________
118
DESCRIPTIVE PART - II Year 2009 Time allowed : 2 Hours Maximum Marks : 30 Attempt any four questions out of the six. All questions carry 7½ marks each.
Q.1
(a)
How is electric energy consumed in a device related to the potential difference and current flowing through it?
Q,2
(b)
What is meant by quantization? How was it ascertained that charge is quantized?
(c)
State Gauss' law of electrostatic.
(a)
What is condenser? Explain its principle?
(c)
Explain the use of condensers in electronic circuits.
(d)
State ohm's law and define resistance of a conductor. On what factors and how does the resistance of a conductor depend?
Q.3
(a)
State Kirchoff's laws and explain their application with the help of examples.
(b)
Explain in the series and parallel combination of resistance.
(c)
What is time constant? Show graphically the dependence of charging and discharging process on time constant.
Q.4
Q.5
(a)
Define self induction and coefficient of self induction
(b)
State Lenz's law. Explain with the help of example.
(c)
What are power and efficiency of an electric motor? Obtain expression for these.
(a)
What is a multi meter? Discuss the design of a multi range voltmeter.
(b)
How is rotating magnetic field produced in a single phase induction motor?
Electrical Circuit and Circuit Analysis
Q.6.
(c)
What is earthing? Explain its importance.
(a)
State and explain reciprocity theorem.
(b)
Define and hybrid parameter h111 and h21.
(c)
What is a four terminal network? Define the h-parameters for such a network.
________
119
120
ELECTRICAL CIRCUIT AND CIRCUIT ANALYSIS PAPER - 111 OBJECTIVE PART- I Year - 2008 Time allowed : One Hour Maximum Marks : 20 The question paper contains 40 multiple choice questions with four choices and student will have to pick the correct one (each carrying ½ mark).
1.
If the force (b) (c)
distance and value of the charges located at different points are doubled, then the acting between them will be: Double (b) Half Unchanged (d) Four time ( )
2.
The unit for electric field intensity is: (b) Newton/Coulomb (c) Volt-meter
(b) (d)
Joule/Coulomb Newton/meter
( )
3.
A charge q is placed on the corner of a cube. The flux emerging out of the cube will be: (b) q/ (b) q/ (c) q/ (d) q/ ( )
4.
The intensity of an electric field at some point distance r from the axis of infinite long pipe having charges per unit length as q will be: Proportional to r2 Proportional to r3 Inversely proportional to r Inversely proportional to r2 ( )
23 24 25 26 5.
6.
The dielectric constant of aluminum is: (b) 1 (c) 10
(b) (d)
Zero Infinity
( )
The charge of same magnitude q are placed at four corners of a square of side a. The value of potential at the centre of square will be:
Electrical Circuit and Circuit Analysis
7.
8.
121
(b)
4kz/a
(b)
(c)
4
(d)
4 ( )
If a soap bubble is positively charged, then its radius: (a) Increases ` (b) Decreases (c) Remain unchanged (d) First increases and then decreases
( )
If a charge Q is brought near another charge Q, then total energy of the system: (a) Remains same (b) Increases (c) Decreases (d) None
( )
9.
If a positive charge is established in an electric field against the Coulomb force then: (a) Work is done by electric field (b) Energy is utilized from some external sources (c) Intensity of electric field decreases (d) Intensity of electric field increase ( )
10.
A point has 10 volt potential, if a charge of + 10coulomb is brought from infinity to that point, then the work done will be: (a) 10 J (b) 100 J (c) 1J (d) 2J ( )
11.
A parallel plate capacitor is given a charge Q. If the separation between the plates is doubled, its capacity will be: (a) Unchanged (b) Zero (c) Doubled (d) Halved ( )
12.
In a charged capacitor, the energy resides: (a) On the positive plate (b) On both the positive and negative plates (c) In the field between the plates (d) Around the edge of the capacitor plates
13.
In a charged capacitor the energy appears as: (a) Magnetic energy (b) Electromagnetic energy (c) Electrostatic energy
( )
122
(d) 14.
Neither electric nor magnetic
( )
The effective capacitance between A and B in the figure is: (a) 1 F (b)
2
F
(c)
1.5
F
(d)
2.5
F
2 F 2 2
15.
16.
17.
F
A
1 F
B
F ( )
The resistance of straight conductor does not depend on its: (a) Temperature (b) Length (c) Material (d) Shape of cross-section
( )
The unit of specific conductance is: (a) Ohm (c) Siemen
(b) (d)
Ohm-M mho-m
( )
The example of non-ohmic resistance is: (a) Copper wire (c) Diode
(b) (d)
Carbon wire Tungsten wire
( )
18.
In which of the following cases the magnetic field is not produced when electric charge (a) Is moving with acceleration (b) Is moving with acceleration (c) Is moving with retardation (d) Is at rest ( )
19.
Magnetic field is produced by the flow the current in a straight wire. This phenomenon is based on: (a) Faraday's (b) Maxwell's law (c) Coulomb's law (d) Oersted law ( )
20.
Unit of magneto motive force is: (a) Ampere/meter (c) Ampere
21.
(b) (d)
Ampere-meter Weber-meter
( )
The direction of lines of force of magnetic field produced due to flow of direct current in a conductor is formed by:
Electrical Circuit and Circuit Analysis
(a) (c) 22.
123
Lenz/s law Faraday's law
(b) (d)
Who discovered magnetic effect of current? (a) Faraday (b) (c) Ampere (d)
Right hand rule Biot-svart's law
( )
Oersted Bohr
( )
23.
The value of magnetic induction B at different points situated on the axis of current carrying wire will be: (a) Zero (b) Maximum (c) Proportional to current (d) None of above ( )
24.
The field intensity due to current I flowing through a straight long wire is proportional to: (a) I (b) I2 (c)
25.
26.
27.
28
When will. (a) (b) (c) (d)
(d)
I/I
( )
current is passed, through two long straight wires in same direction then there be force of repulsion between the wires be force of attraction between the wires Not be any force of attraction between the wires Not be any force in opposite direction mutually
( )
The current flowing in opposite direction mutually. (a) Attract each other (b) Repel each other (c) do not affect each other (d) Attract sometimes and repel sometimes
( )
The value of magnetic induction inside a solenoid along the radius: (a) Is zero (b) decreases with distance from the axis (c) is uniform (d) increases with distance from the axis
( )
The formula for magnetic induction at the centre of current carrying circular coil of radius r is: (a)
(b)
124
(c)
(c)
2
( )
29.
A circular coil A and radius r carries a current I. Another circular coil B of radius 2r carries a current 2/. The magnetic fields at the centers of the circular coils are in the ratio of: (a) 4 :1 (b) 3:1 (c) 2 :1 (c) 1:1 ( )
30.
Magnetic field do not interact with: (a) Stationary electric charges (b) Moving electric charges (c) Stationary permanent magnets (d) Moving permanent magnets `
( )
Diamagnetism is: (a) Distortion effect (b) Orientation effect (c) Both distortion and orientation (d) Cooperative phenomena
( )
The permeability of a substance is zero. Then it is: (a) Diamagnetic (b) Paramagnetic (c) ferromagnetic (d) antiferromagnetic
( )
The function of capacitor in a circuit is to: (a) Pass ac (c) pass dc
( )
31.
32.
33.
34.
35.
(b) (d)
not pass ac not pass ac and dc
In dc circuit, the capacitive reactance of a capacitor is: (a) C (b) 1/ (c) 0 (d)
( )
The phase difference between current and potential in LCR series circuit: (a) is always (b) cannot be zero (c) can be equal to zero (d) will depend on the value of current and the potential
( )
Electrical Circuit and Circuit Analysis
36.
37.
38.
In an L-C-R series resonating circuit the relation between XL and X0 is : (a)
=1
(c)
1 = –1
(d)
( )
LC
(b) (d)
1 2
L
( )
The power loss in series LCR, circuit is :
(c)
40
(b)
What is the ratio of inductive and capacitive reactance in an ac circuit ?
2
(a)
39.
125
Z
(b)
E2/R
(d)
2
R
2
Z
( )
A fuse wire has : (a) a low resistance (c) negligible mechanical strength
(b) (d)
a small diameter a low melting point
( )
A switch can : (a) open a circuit (c) both open and close a circuit
(b) (d)
close a circuit introduce a resistance
( )
Answer key 1. (c) 2. (a)
3. (a)
4. (c)
5. (b)
6. (b)
7. (a)
8. (b)
9. (b)
10. (b)
11. (d)
12. (c)
13. (c)
14. (b)
15. (d)
16. (d)
17. (c)
18. (d)
19. (d)
20. (c)
21. (b)
22. (b)
23. (a)
24. (a)
25. (b)
26. (b)
27. (c)
28. (c)
29. (d)
30. (a)
31. (b)
32. (d)
33. (a)
34. (a)
35. (c)
36. (a)
37. (a)
38. (b)
39. (d)
40. (c)
________
126
DESCRIPTIVE PART - II Year 2008 Time allowed : 2 Hours Maximum Marks : 30 Attempt any four questions out of the six. All questions carry 7½ marks each. Q.1
Q.2
Q.3
(a)
What is coulomb's law? Define electric line of forces.
(b)
What is difference between electric potential and potential difference?
(c)
Calculate the capacitance of series and parallel combination of three capacitors.
(a)
Define Ohm's Law. Explain the factors on which resistivity depends.
(b)
Define electric power and write different units to measure it.
(c)
Discuss the charging and discharging process of RC circuit.
(a)
Explain the basic principle of A.C. generator?
(b)
Explain the basic theory of mutual induction.
(c)
Discuss the step up and step down transformer. Explain the different losses of transformer.
Q.4
(a)
What is Biot- Savart's law and also write the comments on it.
(b)
Discuss the important properties of diamagnetic, paramagnetic and ferromagnetic materials.
Q.5
Q.6
Write short notes on the following: (i)
Kirchhoff's current and voltage low
(ii)
Faraday's law of electromagnetic induction.
(a)
What is electrical safety? Describe the fuses and circuit breakers.
(b)
Describe basic principle of ear thing.
(c)
Write the statement of reciprocity and maximum power transfer theorem.
Electrical Circuit and Circuit Analysis
127
ELECTRICAL CIRCUIT AND CIRCUIT ANALYSIS PAPER - 111 OBJECTIVE PART- I Year - 2007 Time allowed : One Hour Maximum Marks : 20 The question paper contains 40 multiple choice questions with four choices and student will have to pick the correct one (each carrying ½ mark). 1.
If an electron has an initial velocity in the direction different from that of electric field, the path of the electron is : (a) straight line (b) hyperbola (c) ellipse (d) parabola ( )
2.
a charge Q is spread in a spherical volume of radius R. The electric field at a distance r (< R) is given by:
3.
(a)
E=
(c)
E=
(c)
E=
(d)
E=
A charge +Q is placed at the centre of a cube. The amount of electric flux through its entire surface is: (a) (b) (c)
4.
( )
(d)
Zero
( )
A charge q is placed at the centre of the line joining two exactly equal positive charges Q. the system of three charges will be equilibrium if q is equal to: (a) (b) +Q (c)
–Q
(d)
( )
128
5.
A parallel plate capacitor is given a charge Q. If the separation between the plates is doubled, its capacity will be: (b) unchanged (b) Zero (c) doubled (d) halved ( )
6.
In a charged capacitor the energy resides: (c) on the positive plate (d) on both the positive and negative plates (c) in the field between the plates (d) around the edge of the capacitor plates
( )
In a charged capacitor the energy appears as: (b) magnetic energy (b) electromagnetic energy (c) electrostatic energy (d) neither electric nor magnetic
( )
7.
8.
Two condensers of capacitor C1 and C2 charged to potential V1 and V2 are joined by a wire. The loss of energy E is: (b) E = (C1 + C2) (V1–V2)2 (b) (c)
9.
10.
(d)
On heating the dielectric constant of an insulator: (e) remains constant (b) (c) decreases (d)
( )
A charge on each capacitor in the circuit is : 1 F
4V
(a) (c) 11.
increase nothing can be predicted
1 3
C C
IV ++ 2+ + F
+ + (b) (d)
2 4
C C
The resistance of a straight conductor does not depend on its:
( )
Electrical Circuit and Circuit Analysis
(a) (c) 12.
13.
14.
16.
17.
18.
19.
(b) (d)
length shape of cross section
( )
A flow of 107 electrons per second in a conducting wire constitutes a current of: (a) 1.6 X 10–26 A (b) 1.6 X 1012 A (c) 1.6 X 10–12 A (d) 1.6 X 1026 A
( )
Indentify the set in which all the materials are good conductors of electricity. (a) Cu, Ag and Au (b) Cu, Si and diamond (c) Cu, Hg and NaCL (d) Cu, Fe and Hg
( )
When a current flows in a conductor, the order of magnitude of drift velocity of electrons through it is: (a) 1010 m/s (b) 10–2 m/s (c)
15.
temperature material
129
1010 cm/s
(d)
10–7 cm/s
( )
The temperature co-efficient of resistance is positive for: (a) Carbon (b) Copper (c) Si (d) Ge
( )
The temperature co-efficient of resistance is negative for: (a) Ge (b) Copper (c) Aluminum (d) Nickel
( )
The example of non-ohmic resistance is: (a) Copper wire (c) Diode
( )
(b) (d)
Carbon resistance Tungsten wire
Ampere's line integral low is: (a)
B.dI =
(b)
B.dI =
(c)
B.dI =
(d)
B.dI =
I ( )
The magnetic induction at the centre of a square loop of wire of side 'a' carrying I is: (a) B= (b) B=
current
(c)
( )
B=
(d)
B=
130
20.
Two parallel wires carrying currents in the same direction attract each other because of: (a) potential difference between them (b) mutual difference between them (c) electric forces between them (d) magnetic forces between them ( )
21.
Magnetic field do not interact with: (a) stationary electric charges (b) moving electric charges (c) stationary permanent magnets (d) moving permanent magnets
22.
The time constant of the circuit is: (a) 3 second (b) 5 second (c) 1.5 second (d) 2 second
( ) 3 µF 1
m
2V
( ) 23.
24.
25.
26.
27.
Diamagnetism is a: (a) distortion effect (c) both distortion and orientation
(b) (d)
orientation effect cooperative phenomena
( )
Paramagnetism is a: (a) distortion effect (c) neither distortion nor orientation
(b) (d)
orientation effect cooperative phenomena
( )
Fe3O4 is: (a) paramagnetic (c) ant ferromagnetic
(b) (d)
ferromagnetic ferromagnetic
( )
The phenomenon of hysteresis is: (a) lack of retraceability (b) lack of negative susceptibility (c) lack of small susceptibility (d) lack of using direct current for a superconductor, the value of susceptibility is:
( )
Electrical Circuit and Circuit Analysis
(a) (c) 28.
29.
30.
31.
32.
33.
34.
35.
zero –1
131
(b) (d)
1 infinity
( )
The spin- spin interaction in a ferromagnetic substance is: (a) strong (b) weak (c) zero (d) very weak
( )
I Wb/m2 equals: (a) 1 Gauss (c) 103 Gauss
( )
(b) (d)
102 Gauss 104 Gauss
The heating of the large transformers is due to: (a) the heat generated by current (b) hysteresis alone (c) both the hysteresis and heating effect of current (d) none of the above
( )
Lenz's law is a consequence of the law of conservation of: (a) charge (b) mass (c) momentum (d) energy
( )
The back e.m.f. in d.c. motor is maximum when: (a) the motor has picked up maximum speed (b) the motor has just started moving (c) the speed of the motor is till on the increase (d) the motor has just been switched off
( )
A 100 mH coil carries a current of I A. energy stored in its magnetic field is: (a) 1J (b) 0.5 J (c) 0.05 J (d) 0.1 J
( )
Eddy currents are produced when: (a) a metal is kept in a varying magnetic field (b) a metal is kept in a steady magnetic field (c) a circular coil is placed in a magnetic coil (d) a current is passed through a circular coil
( )
Lamination of transformer core: (a) eliminates heating due to eddy current (b) eliminates magnetic field due to eddy current
132
(c) (d) 36.
37.
38.
eliminates both heating and magnetic field due to eddy current none of the above
Ina transformer Vp = 220 V and Vs = 22 v. it runs a machine of 220 current in the primary coil is: (a) 1A (b) 0.1 A (c) 0.01 A (d) 1mA
( ) resistance. The
( )
In LCR parallel circuit: (a) I is minimum, Z is minimum (b) I is minimum, z is maximum (c) I is maximum, Z is minimum (d) I is maximum, Z is maximum
( )
In comparison to d.c. transmission losses in a.c. are: (a) high (b) low (c) negligible (d) none of the above
( )
39.
When frequency of an LCR - series circuit increases, the impedance Z: (a) First decreases and then increases (b) first increases and then decreases (c) increases uniformly (d) decreases uniformly ( )
40.
Earthing is used: (a) As a neutral line (c) to reduce voltage fluctuation
(b) (d)
to save power as a safety measure
( )
Answer Key 1. (d) 2. (d)
3. (a)
4. (a)
5. (d)
6. (c)
7. (c)
8. (d)
9. (c)
10. (b)
11. (d)
12. (c)
13. (a)
14. (b)
15. (b)
16. (a)
17. (c)
18. (c)
19. (d)
20. (d)
21. (a)
22. (a)
23. (a)
24. (b)
25. (d)
26. (a)
27. (c)
28. (b)
29. (d)
30. (c)
31. (d)
32. (a)
33. (c)
34. (a)
35. (c)
36. (c)
37. (b)
38. (b)
39. (a)
40. (d)
________
Electrical Circuit and Circuit Analysis
133
DESCRIPTIVE PART - II Year 2007 Time allowed : 2 Hours Maximum Marks : 30 Attempt any four questions out of the six. All questions carry 7½ marks each. Q.1
Q.2
Q.3
(a)
What is electric line force? What is its importance?
(b)
What is the importance of gauss law? Explain the electrostatic shielding?
(a)
What is the function of dielectric in capacitor?
(b)
Calculate the capacitance of series and parallel combination of their capacitors.
(a)
What is solenoid? Give the magnitude of magnetic field developed at a
point
well inside a solenoid carrying current. (b) Q.4
Q.5
Q.6
What are the hysteresis curve? What are their uses for a given material?
Write short note on the following: (a)
A.C. generator
(b)
Biot-Savart's law
(c)
Kirchhoff's current and voltage law
Define the following physical quantities: (a)
Magnetic Flux
(b)
Intensity of magnetizing field
(c)
Permeability
(d)
Magnetic Susceptibility
(e)
Relative Permeability
(a)
Write statement of Thevenin's and Norton theorems?
(b)
What is the maximum power that can be delivered by a generator of e.m.f.E. and internal resistance r when the load resistance is R? __________
134
ELECTRICAL CIRCUIT AND CIRCUIT ANALYSIS PAPER - 111 OBJECTIVE PART- I Year - 2006 Time allowed : One Hour Maximum Marks : 20 The question paper contains 40 multiple choice questions with four choices and student will have to pick the correct one (each carrying ½ mark). 1.
2.
3.
4.
5.
Which of the following experiment verifies quantization of charge? (a) Rutherford (b) Millikan's oil drop (c) Discharge of gases (d) Faraday's electrolysis
( )
Which is not a property of conductors? (a) Have free electrons (b) Resistance increases with temperature (c) Negligible bank gap (d) Contains electron - hole pairs
( )
Which is wrong about coulomb's force? (a) It is a long range force (b) it follows inverse square law (c) It does not depend on medium (d) It may be attractive as well as repulsive
( )
Which relation violates the law of conservation of electric charge? (a) n p +e– +v (b) P n + e+ + v (c) e+ e(d) e+ e+
( )
A charge + Q is placed at the centre of a cube, the amount of electric flux through its entire surface is: (a) (b) (c)
(d)
Zero
( )
Electrical Circuit and Circuit Analysis
6.
135
The electrostatic potential energy of a system of two stationary point charges + q1 and - q2 are separated by a distance r is given by: (a) (b) (b)
7.
(d)
( )
The equivalent capacitance of the circuit between A and B is: (a)
3C
F
A
C µF
C µF B
(b) C µF
(c) (d) 8.
9.
( ) When dielectric material is inserted between the plates of a capacitor its capacitance (a) decreases (b) increase (c) remains constant (d) reduces to zero ( ) The net current 'I' in the circuit is: (a) 1.5 A (b) (c) (d)
0.8
0.4
2.4
1.2
( ) 10.
The time constant of the circuit is: (a) 3 Second (b) 1.5 Second (c) 6 Second (d) 2 Second
1M
3 µF
2 µF
( )
136
11.
The magnetic field at a distance r (r>>1) due to a bar magnet of pole strength m at an axial point P is: r (a) (b)
m
P
(c) S
N 2I
(d)
12.
13.
14.
Field due to a current carrying coil at the centre is: (a)
(b)
(c)
(d)
( )
The current between two infinite straight conductors separated by a distance 10 m are 2 A and 4 A respectively. The force per unit length between them is: (a) 1.8 X 10–3 N/m attractive (b)
1.6 X 10–3 N/m repulsive
(c)
3.2 X 10–3 N/m attractive
(d)
3.2 X 10–3 N/m repulsive
( )
The magnetic field inside a solenoid of radius 'R' and turn density 'n' is given by: (a) (b) (c)
15.
( )
(d)
( )
According to faraday's law of e.m. finduction the inducted e.m.f. 'e' is: (a)
(b)
(c)
(d)
( )
Electrical Circuit and Circuit Analysis
16.
137
In the given resistor circuit, the current flowing through the resistance CD will be: (a) (b) (c)
4
C 2
D
I
4 10 V
(d) ( ) 17.
18.
19.
20.
21.
22.
23.
The commercial unit of electrical energy is: (a) Joule (b) (c) Kilo Watt (d)
Watt Kilo Watt hour
( )
The unit of capacitance is: (a) Farad (c) Henry
Ohm Newton
( )
(b) (d)
A diamagnetic material contains: (a) One unpaired (b) More than one unpaired electron (c) Only paired electrons (d) None of the above The time constant of an L R circuit is given by: (a) R/L (b) (c) RL (d)
( )
L/R R2 L
( )
In a pure capacitor: (a) current leads the e.m.f. by phase 90o (b) current legs behind the e.m.f. by phase 90o (c) current of e.m.f. are always in the same phase (d) current and e.m.f. are always opposite phase
( )
In and ideal A.C. circuit the power is consumed in: (a) Resistance (b) Capacitance (c) Inductance (d) LC Circuit
( )
The resonant frequency of series LCR circuit consists of R = 100 mH is:
and L= 100
138
(a) (c) 24.
25.
26.
27.
28.
29.
10 Hz 500 Hz
(b) (d)
100Hz 5000 Hz
( )
The function of d.c. motor is: (a) to covert energy to electrical energy (b) to convert electrical energy to mechanical energy (c) to covert electrical energy to magnetic energy (d) to convert magnetic energy to electrical energy
( )
Which is not a characteristic of ferromagnetic material? (a) High value of magnetic permeability (b) Positive value of magnetic susceptibility (c) Negative value of magnetic susceptibility (d) Attracted by exterior magnetic field
( )
The average value of an A.C. over one time period is: (a) (b) 2 (c) zero (d) infinity
( )
A multi meter cannot be used to measure: (a) current (c) resistance
(b) (d)
voltage capacitance
( )
A Thevenin equivalent circuit consist of: (a) A voltage source (c) Both the sources
(b) (d)
A current source None of the above
( )
Which is not a vector quantity? (a) Electric field intensity (E) (c) Electric potential
(b) (d)
Magnetic flux density Coulomb force
( )
30.
In a transformer the number of turns in primary and secondary coils are 5000 and 500000 respectively. If an AC voltage of 200 V is applied across the primary coil then the output voltage across secondary coil will be: (a) 200 kV (b) 20 kV (c) 20 V (d) 200 V ( )
31.
The unit of L is: (a) Henry
(b)
Farad
Electrical Circuit and Circuit Analysis
(c) 32.
33.
139
Ohm
(d)
The electric potential over an ear thing wire is: (a) 220 V (b) (c) 0V (d)
Joule
( )
440 V 220 kV
( )
4A Zero
( )
The current in branch AB in the given circuit is: 2A A
B
C
D
4A
(a) (c) 34.
2A 6A
(b) (d)
The charge stored in the capacitor shown in figure is: 2 µF
2 volt
(a) (c) 35.
36.
2 C 1C
(b) (d)
The coil of an electrical heater is made up of: (a) Copper (b) (c) An alloy (d)
4 1
C C
( )
Iron Aluminum
( )
When an iron rod in inserted inside an inductance coil, its inductance: (a) Increases (b) Decreases (c) First increases then decreases (d) Does not change
( )
37.
A 100 watt bulb is switched on for 6 hours, then the electrical units consumed by it are: (a) 600 Units (b) 0.06 Unit (c) 0.6 Unit (d) 1.0 Unite ( )
38.
A room temperature which of the following is an insulator? (a) Silver (b) Diamond (c) Gold (d) Silicon
( )
140
39.
The direction of current induced in the loop abed in given circuit is: (a)
Clock wise
(b)
anticlockwise
(c)
upwards
(d)
downwards
A
B
40.
The force on a charge + q in an electric field E: (a) along the E (b) E (c) to (d)
x x x x x x x x x x x x
x x x x x x x x x x x x
x x x x x x x x x x x x
x x x x x x x x x x x x
x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x
( )
opposite to E along a circular path
( )
Answer Key 1. (b) 2. (d)
3. (c)
4. (d)
5. (a)
6. (d)
7. (c)
8. (b)
9. (a)
10. (a)
11. (a)
12. (a)
13. (b)
14. (a)
15. (a)
16. (c)
17. (d)
18. (a)
19. (c)
20. (b)
21. (a)
22. (a)
23. (c)
24. (b)
25. (c)
26. (c)
27. (d)
28. (a)
29. (c)
30. (b)
31. (c)
32. (c)
33. (c)
34. (b)
35. (c)
36. (c)
37. (c)
38. (b)
39. (b)
40. (a)
_________
Electrical Circuit and Circuit Analysis
141
DESCRIPTIVE PART - II Year 2006 Time allowed : 2 Hours Maximum Marks : 30 Attempt any four questions out of the six. All questions carry 7½ marks each.
Q.1
Q.2
Write statements of the following laws: (i)
Coulomb's law
(ii)
Gauss's law of electrostatic
(iii)
Kirchhoff's voltage law
(iv)
Biot-Savart's law
(v)
Ohm's law
(a)
Define the following physical quantities and write their units:
(i)
Electric potential
(ii)
Capacitance
(iii)
Resistivity
(c)
What do you understand by the quantization of charge? Write the magnitude of minimum possible stable charge.
Q.3
(a)
Write the faraday's law of e.m.f. induction?
(b)
Taking three resistances of magnitude R1, R2, R3 Draw their series and combination circuits. Write the formula for effective resistance.
Q.4
Draw the block diagram of the following electrical devices. (a)
A.C. generator
(b)
D.C. motor
parallel
142
(c)
3- induction motor
Q.5
Which materials are used in house wiring? Draw wiring layout for a computer lab.
Q.6
(a)
Write statements of maximum power transfer theorem and norton's theorem.
(b)
Draw phasor diagrams showing phase difference between V and I in circuits containing pure L and pure C along with an A.C. source.
Electrical Circuit and Circuit Analysis
143
Key Terms Coulomb’s law: Coulomb’s law is the statement that the force F between two electrical charges q1 and q2 separated by a distance r is F = 1/ 4πεo (q1q2/ r2 ) where εo is the permittivity of a vacuum, equal to εo = 8.8542×10-12 F/m. electric field: If a small amount of charge experience a force, there is an electric field in the vicinity. Electric field E is defined in terms of electrostatic force F that would be exerted on positive test charge qp placed in the field: E→ = F→ qp SI unit for electric field is N C-1, or V m-1.
potential energy Potential energy (Ep) is the energy stored in a body or system as a consequence of its position, shape, or state (this includes gravitation energy, electrical energy, nuclear energy, and chemical energy). Gauss’ law for electrostatics: Gauss’ law states that the net flux of electric field, Φ, through an imaginary closed surface, S, - a Gaussian surface - is equal to the net charge, q, inside that closed surface: Φ=q where electric flux Φ through Gaussian surface is given by: Φ = εo ∫ S E→ · dS→ ε0 is the permittivity constant and dS is a surface element.
144
Battery - A combination of two or more chemical cells connected together electronically to produce electrical energy. Battery - A combination of two or more chemical cells connected together electronically to produce electrical energy. Capacitor - An electrical device having Capacitance Current Limiting Fuse - A fuse designed to reduce damaging extremely high current Current Transducer - A transducer used for the measurement of A.C. current. Current Transformer - A transformer used to measure the amount of current flowing in a circuit by sending a lower representative current to a measuring device such as a meter
Kilowatt 1,000 watts of electricity. Kilowatt hour One kilowatt of electricity produced or used in one hour.
Capacitor: A capacitor is a storage tank for electrical energy. In DC applications it blocks DC current and in AC applications it regulates AC current. Capacitance: Capacitance is the property of a capacitor that defines its ability to store an electrical charge (or energy) when a given voltage is applied. The international unit of measurement for capacitance is Farad (or microfarads), which is named after the famous English inventor Michael Faraday (1791-1867). Dielectric: Dielectric is the material used as the insulating medium between the plates of a capacitor. Dielectric Constant - A number that describes the dielectric strength of a material relative to a vacuum, which has a dielectric constant of one.
Electrical Circuit and Circuit Analysis
145
Three Phase - Three-phase refers to one circuit consisting of three conductors where the current and voltage in each conductor (phase) is 120° out of phase with each other phase.
Electrical Current Definition: Electrical current is a measure of the amount of electrical charge transferred per unit time. It represents the flow of electrons through a conductive material.
Resistance Electrical resistance is a measure of how hard it is for a current to pass through a given material. It is similar to the way that it is harder for you to walk through water than air. It is usually measured in Ohms
Ohm :The Ohm is the unit of electrical resistance. Alternating Current (AC): A type of electrical current in which the direction of the flow of electrons switches back and forth. In the US, the current that comes from a wall outlet is alternating; it cycles back and forth sixty times each second. The current that flows in a flashlight, on the other hand, is direct current (DC), which does not alternate.
Direct Current (DC): Current which moves in a single direction in a steady flow. Normal household electricity is alternating current (AC) which repeatedly reverses its direction. However, many electronics devices require DC, and therefore must convert the current into DC before using it. Diodes are used to convert AC to DC.
magnetic field — area of force that exists around a magnet or a current-carrying conductor. magnetism — the force of attraction between an object and a magnet, which pulls the object toward the magnet.
Frequency: Frequency is the number of complete cycles per unit of time of any periodically varying quantity, such as alternating voltage or current. It is usually expressed as (Hz) Hertz or CPS (cycles per second).
alternating current: electric current that reverses direction periodically, usually many times per second.
146
ammeter: an instrument used for measuring the electrical current flow in a portion of a circuit. galvanometer: an instrument for measuring a small electric current ohmmeter: an instrument for measuring electric resistance. resistor: a device used in electric circuits to limit the current flow or to provide a voltage drop. transformer: a magnetic coupling device in an AC circuit; they are capable of changing voltages as needed. voltmeter: an instrument used for measuring the potential difference between two points in volts. the motion of electrons through a conductor. Electricity Volt*
the unit of electromotive force or electric pressure, akin to water pressure in pounds per square inch.
Watt*
the electrical unit of power or rate of doing work. Farad - The capacitance value of a capacitor of which there appears a potential difference of one volt when it is charged by a quantity of electricity equal to one coulomb. Fuse - A device installed in the conductive path with a predetermined melting point coordinated to load current. Fuses are used to protect equipment from over current conditions and damage.
Transformer equipment vital to the transmission and distribution of electricity designed to increase or decrease voltage. Eddy Current - The current that is generated in a transformer core due to the induced voltage in each lamination. It is proportional to the square of the lamination thickness and to the square of the frequency. Electromotive Force - Potential causing electricity to flow in a closed circuit. Induced Current - Current in a conductor resulting from a nearby electromagnetic field. Induced Voltage - A voltage produced in a circuit from a nearby electric field.
Circuit - A system of conducting media designed to pass an electric current Maximum power transfer theorem A theorem used to determine the load resistance necessary to ensure maximum power transfer to the load.
Norton's theorem A theorem that permits the reduction of any two-terminal linear dc network to one having a single current source and parallel resistor.
Electrical Circuit and Circuit Analysis
147
Superposition theorem A network theorem that permits considering the effects of each source independently. The resulting current and/or voltage is the algebraic sum of the currents and/or voltages developed by each source independently.
Thevenin’s theorem A theorem that permits the reduction of any two-terminal, linear dc networks to one having a single voltage source and series resistor.
Wire - A strand or group of strands of electrically conductive material, normally copper or aluminum.
