Phy 1 (6)
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Phy...
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http://www.rpmauryascienceblog.com/
Q.1.
As shown in the figure, a metal rod makes contact with a partial circuit and completes the circuit. The circuit area is perpendicular to a magnetic field with B = 0.25T. If the resistance of the total circuit is 3, what force is needed to move the rod with a constant speed of 4 m/s as indicated in the figure ?
B = 0.25 T(into page) 50cm v = 4m/s
Q.2.
A solenoid has an inductance of 10 H and a resistance of 2 . It is connected to a 10 V battery. 1 How long will it take for the magnetic energy to reach of its maximum value? 4
Q.3.
A conducting ring of radius r is rolling without slipping with a constant angular velocity . If the magnetic field strength is B and is directed into the page then find emf induced across PQ.
Q.4.
Q.5.
Q.6.
There is a circular region of radius R in which dB magnetic field is varying as . A horizontal rod dt AB of length L is placed as shown in figure. Point C is centre of the circle and also the mid point of rod. Find the potential difference between A and B.
x
x
x x
A conducting loop has an area A = 800 cm2 and incorporates a capacitor with capacitance C = 10.0 F. It is placed in a uniform magnetic field perpendicular to the magnetic induction lines, the magnetic induction varying as B = (8 + 5t) 10––2T. Determine : (a) The maximum charge on the capacitor (b) The maximum energy stored in the capacitor (c) Which plate (A or B) will be charged positively. The network shown in the adjacent figure is a part of a
x x
P
Q
A x x x x
x x
C B x x x x x x x x x R
x
x
x
A
C B
x
x x
x
x
x x
x x
x
x
x
x
x
x
x
x
x x
x
http://www.rpmauryascienceblog.com/ complete circuit. What is the potential difference V B VA, when the current I is 5A and is decreasing at a rate of 103 A/s? Q.7.
15V
1 A
Find the current provided by the source immediately after the switch is closed at t = 0 and also at t = infinity.
5mH
I
B
L= 1 mH
R2 = 10
R1 = 10 Sw E = 10 V
Q.8.
Find the average current in terms of I0, in the graph as shown in the figure
current I0 time
T 4
Q.9.
T 2
3T 4
T
A metallic rod of length & resistance R is free to rotate about one of its ends over a horizontal smooth, rigid circular metallic frame of radius in an inward magnetic field of induction B. The circuit is completed by means of a conducting wire connected between the centre O and the point on the ring. What torque should be applied by an external agent to rotate the rod with constant angular velocity? What is the power expenditure of the external agent?
O
B
wire
Q.10. In the circuit shown, current at the given instant is 1 amp, and it is decreasing at a constant rate of 103 amp/sec., Find VA-VB between the terminals A and B.
B
A R=10
E=4v
L=10 mH
Q.11. A solenoid of inductance 100 mH and resistance 20 is connected to a cell of emf 10 V at t = 0. Find the energy stored in the inductor when the time t = 5 ln2 milliseconds. Q.12. A metallic cylindrical rod PQ slides without friction on a rectangular circuit composed of perfectly conducting wires fixed on inclined plane as shown in the figure. A vertical magnetic field B exists in the region of the above mentioned setup. Find the velocity of the rod PQ when it starts moving without any acceleration ? Q.13. (b) A semicircular wire frame ABC is moved along it's plane in magnetic field with velocity V as shown in figure, find emf developed a cross AC.
B
Q P v
L
x x x x x B x x x x x x x x x x x
A x xR x x x x xC x
x x x x x x x x
V
http://www.rpmauryascienceblog.com/ Q.14. A rectangular flat loop of wire with dimensions and b has N turns and a total resistance R. The loop moves with constant velocity v from position PQRS to PQRS through a region of constant magnetic field B as shown in figure (a) Plot the graph of the flux linked with loop vs x. (Where x is the distance moved by the loop) (b) Plot the graph of the emf induced in the loop vs x. Q.15. A conducting rod makes contact with a partial circuit and completes the circuit as shown. The circuit area is perpendicular to a magnetic field with B = 0.25 T. If the resistance of the total circuit is 5 , how large force is needed to move the rod as indicated with a constant speed of 4 m/s apart from the force F = 1/ 80 N already acting on it in the direction shown ?
P
Q
× × × × × × ×
P
Q
× × × × × × ×
× × × × × × × × × × × × × ×
S
R
b
S
2b
x=0
50 cm
b
R
x = 2b
B = 0.25 T v = 4m/s F
Q.16. A solenoid of inductance 100 mH and resistance 20 is connected to a cell of emf 10 V at t = 0. Find the energy stored in the inductor when the time t = 5 ln2 ms. Q.17. A wheel with six spokes is positioned perpendicular to a uniform magnetic field B of magnitude 0.5 T. The field is directed into the plane of the paper and is present over the entire region of the wheel as shown in the figure. When the switch S is closed, there is an initial current of 6A between the axle and the rim; and the wheel begins to rotate. The resistance of the spokes and of the rim is negligible. (a) What is the direction of rotation of the wheel? (b) The radius of the wheel is 0.2 m . Calculate the initial torque on the wheel . Q.18. A constant potential difference of 60 V is suddenly applied to a coil which has a resistance of and a self inductance of 8mH. At what rate does the current begin to 30 rise? What is the current at the instant the rate of charge of current is 500 A/s ? What is the final current ? Q.19. As shown in the figure, a metal rod makes contact with a partial circuit and completes the circuit. The circuit area is perpendicular to a magnetic field with B = , how large force is 0.15T. If the resistance of the total circuit is 3 needed to move the rod as indicated with a constant speed of 2 m/s ?
S
8 mH
30
60 V
B = 0.15 T(into page) 50 cm v = 2m/s
Q.20. A very small circular loop of radius a is initially coplanar and concentric with a much larger circular loop of radius b (a < < b). A constant current i is passed in large loop, which is kept fixed in space, and the small loop is rotated with angular velocity about a diameter. The resistance of the small loop is ‘R’. If its self inductance is negligible. Find (a) current in small loop as a function of time.
http://www.rpmauryascienceblog.com/ (b) induced emf in large loop as a function of time. Q.21. A conducting rod 'OA' of mass 'm' and length 'l' is Y x x x x x x kept rotating in a vertical plane about a fixed x horizontal axis passing through 'O'. The free end 'A' x x A x x is arranged to slide on a fixed conducting ring S without any friction. A uniform and constant x x x X O magnetic field 'B' perpendicular to the plane of B x x x rotation is applied. The point 'O' and the point 'C' x R (on the ring) are connected by a series combination C x x x x x x of 'R' a resistor 'R' and an inductor 'L' through a switch 'S'. The angular frequency of the rod is . Initially the switch is opened. Neglect any other L resistance. (a) Find the e.m.f. induced across the length of the rod. (b) The switch is closed at time t = 0 . (i) Obtain an expression for the current in the resistor as a function of time (ii) In the steady state find the torque needed to maintain the constant angular speed of the rod. The rod was initially along the positive X-axis. Q.22. The arrangement shown is placed in a uniform vertical field of strength 3 tesla. Initially both the rods are at rest. The system is released at t = 0. Find the velocity of the rod of mass m as a function of time. Neglect friction. Take m = 1 kg.
B= 3 Tesla R = 54 m
= 1m. 2m
3m
Q.23. In the co-ordinate system shown in the figure magnetic field is directed along negative z-axis and its magnitude varies B0 as B = , where B0 is a positive x constant. A square loop ABCD of side ‘a’ and resistance per unit length ‘’ is moved with constant speed v with its plane parallel to x-y plane. Initially side AB was on the y-axis. Find the current induced in the loop as a function of time. Q.24. A long conductor is placed in horizontal plane carrying current (3 + 4t2). Assume loop having side 0.25 m is placed in same plane at a distance 1m from conductor as shown in figure. Loop is connected by an inductor, having inductance 5 H. Find current in inductor as function of time assume t = 0, current starts flowing in conductor.
Y
B
A
D X
Z
0.25 m
I =(3+4t2)
C
L =5H 1m
0.25 m
http://www.rpmauryascienceblog.com/ Q.25. A conducting square loop of side a2 is rotated in a uniform magnetic field B about P in the plane of the paper as shown in the figure. (a) Find the induced emf between P and Q and indicate the polarity of the points P and Q. (b) If a resistance R is connected between P and Q, determine the current through the resistor.
B
Q
Q.26. A ring of radius R made up of a conducting wire whose cross section a is placed in a magnetic field perpendicular to the plane. The magnetic field varies with time as B = B0 sin 2ft. where B0 is a constant.
x
x
x x
P
x
x x x x x x x x x R x x x x x x x x x x x x
x x x x x x
(a) find the induced emf in the ring. (b) find the resistance of the ring if the resistivity of the material is . (c) What is instantaneous power loss due to current in the ring? (Ignore the self induced currents in the ring.) M Q.27. Two long parallel horizontal rails, a distance 20 cm apart, each B having a resistance 0.2 /m per unit length, are joined at one R x x x end by a resistance 500 . A perfectly conducting rod MN of x x x F d mass 0.2 kg is free to slide along the rails without friction. x x x There is a uniform magnetic field of induction 50T normal to the x x x FM plane of the paper and directed into it. A variable force F is N x applied such that a constant current, 2 Amp, flows through R. (a) Find the magnetic force FM on the rod, and the induced emf as a function of the distance, 10 cm. (b) Find the velocity of the rod, and the applied force F as a function of the distance 10 cm of the rod from R. (c) What fraction of the work done by F is converted into heat?
Q.28. In the figure shown, Resistance per unit length of a square loop of side ‘a’ is . Find the current in the loop as a function of time if x varies as x = vt, where v is a constant.
I
v x
Q.29. An inductor of inductance 2.0 mH is connected across a charged capacitor of capacitance 5. F, and resulting LC circuit is set oscillating at its natural frequency. Let Q denote the instantaneous charge on the capacitor, and I the current in the circuit. C. It is found that the maximum value of Q is 200 dI (a) When Q = 100 C, what is the value of dt (b) When Q = 200 C, what is the value of I ? (c) Find the maximum value of I.
http://www.rpmauryascienceblog.com/ (d) When I is equal to one half its maximum value, what is the value of |Q| ? Q.30. (a) A closed circuit in steady state consists of a battery of 20 volt and a coil of inductance 0.2 H and total resistance of the circuit equals 2 . At the moment t = 0 the inductance of the coil is suddenly decreased to 1/10 times. Find the time dependent expression for the current. (b) A square loop of side 1m and a long straight conductor carrying a current of 5A are located in the same plane. Resistance of the loop is 1 . The loop is turned through an angle of 1800 about an axis PQ. Axis PQ is at a distance of 3m from the current carrying conductor. Find the electric charge having flown through the loop.
P 5A Q
1m 3m
Q.31. A constant potential difference of 60 V is suddenly applied to a coil which has and a self inductance of 8mH. At what rate does the resistance of 30 current begin to rise? What is the current at the instant the rate of change of current is 500 A/s? What is the final current ?
8 mH
30
60 V
Q.32. An inductor of inducance 2.0 mH is connected across a charged capacitor of capacitance 5.0F and the resulting LC circuit is set oscillating at its natural frequency. Let Q denotes the instantaneous charge on the capacitor and I the current. It is found that the maximum value of Q is 200 C. (a) When Q = 100 C, what is the value of | dI/dt |? (b) When Q = 200 C what is the value of I (c) When I is equal to one-half its maximum value, what is the value of | Q | Q.33. In the above figure, PQ is an infinite wire carrying current I as shown. MN is a rigid conducting rod that can slide smoothly on parallel rails XX and YY. MN was coincident with resistance R at t = 0. Find the force required to pull rod MN away from PQ with a constant velocity ‘v 0’ as a function of time.
Q X
M
X
I d
Y
N
Y
P a
Q.34. An L-C circuit consist of an inductor with L = 0.09 H and a capacitor of C = 4.00 10-4 F. The initial charge on the capacitor is 5.00 C and the initial current in the inductor is zero. (a) Find the value of maximum current in the inductor. (b) When the current in the inductor has half its maximum value, what is the charge on the capacitor.
http://www.rpmauryascienceblog.com/ Q.35. A charge particle of charge q and mass m is projected with velocity v in x-y plane making an angle with the x-axis, from the origin of coordinates. A uniform magnetic field B also acts along the x-axis. Find the position coordinates of the particle at a time m . t 2qB
Q.36. Two conducting rails separated by a distance are joined at the top by a resistance R. The rails are inclined at an angle with horizontal. A conducting wire MN of mass m and length . Slides without friction on rails with constant speed v. The conducting wire and rails have no resistance. A uniform magnetic field B acts horizontally and perpendicular to the wire MN. Find value of the magnetic field B. Q.37. (a) The current in a certain circuit varies with time as shown in figure. Find the average current and the rms current in terms of I0.
Y
v m q
X
B Z
R
M
B
N v
i0
t
2
-i0
(b) A voltage source v = 10 sin 2t volt is connected to the circuit as shown in the figure. Find the energy dissipated through the resistor in first 0.5 sec ?
Q.38. Calculate the (i) impedance (ii) current (iii) phase (iv) power factor for the circuit shown in the figure
~
1 k
V = 10 sin 2t
8 XC = 20 XL = 14
~ 220 V, 60 Hz
Q.39. A thermocole vessel contains 0.5 kg of distilled water at 300 C. A metal coil of area 5 10-3 m2, number of turns 100, mass 0.06 kg and resistance 1.6 is lying horizontally at the bottom of the vessel. A uniform, time varying magnetic field is set up to pass vertically through the coil at the time t = 0. The field is first increased from zero to 0.8 T at a constant rate between 0 and 0.2. s and then decreased to zero at the same rate between 0.2 and 0.4 s. This cycle is repeated 12000 times. Make sketches of the current through the coil and the power dissipated in the coil as functions of time for the first two cycles. Clearly indicate the magnitudes of the quantities on the axes. Assume that no heat is lost to the vessel or the surroundings. Determine the final temperature of the water under thermal equilibrium. Specific heat of the metal = 500 Jkg -1K-1 and the specific heat of water = 4200 Jkg-1K-1. Neglect the inductance of the coil.
http://www.rpmauryascienceblog.com/ Q.40. An equilateral triangular conducting loop of side a and resistance R is placed adjacent to a current carrying long straight wire in same plane, such that distance between wire and side of loop is d. Current is given as I = I0 sin t, then find the current in the loop as function of time.
I = I0 sin t a d
Q.41. A coil of inductance L connects the upper ends of two vertical copper bars separated by a distance . A horizontal conducting connector of mass m starts falling with zero initial velocity along the bars without loosing contact with them. The whole system is located in a uniform magnetic field B perpendicular to the plane of the bars. Find the law of motion x (t) of the connector.
Q.42. A loop is formed by two parallel conductors connected by a solenoid with inductance L and a conducting rod of mass m which can freely (without friction) slide over the conductors. The conductors are located in a horizontal plane in uniform vertical magnetic field B. The distance between the conductors is . At the moment t = 0, the rod is imparted an initial velocity v 0 directed to the right. (a) Show that rod will oscillate simple harmonically. (b) Find angular frequency of simple harmonic motion. Q.43. Two parallel vertical metallic rails AB and CD are separated by 1m. They are connected at the two ends by resistances R1 and R2 as shown. A horizontal metallic bar L of mass 0.2 kg slides without friction, vertically down the rails under the action of gravity. There is a uniform horizontal magnetic field of 0.6 T perpendiculars to the plane of rails. It is observed that when the terminal velocity is attained. The powers dissipated in R1 and R2 are 0.76 W and 1.2 W respectively. Find the terminal velocity of the bar L and the value of R1 and R2. Q.44. Find the frequency of the LC circuit shown in figure (a) L L L C
v0 m
R1 A
C
L B
R2
D
x
http://www.rpmauryascienceblog.com/ (b) A circuit containing a two position switch S is shown in figure. (i) The switch S is in position 1. Find the potential difference VA - VB and the rate of production of joule heat in R1. (ii) If now the the switch S is put in position 2 at t = 0, find the time when the current in R4 is half the steady value. Also calculate the energy stored in the inductor L at that time.
R3
C
2
1 2
2F
R1
E1
2
12V E2
S A
3V
R5
1
R2 B 2
R4
3
10 mH
Q.45. A metal rod OA of mass m and length r is kept rotating with a constant angular speed in a A vertical plane about a horizontal axis at the end S O. The free end A is arranged to slide without X O friction along a fixed conducting circular ring in the same plane as that of rotation. R A uniform C and constant magnetic induction B is applied perpendicular and into the plane of rotation as shown in figure. L An inductor L and an external resistance R are connected through a switch S between the point O and a point C on the ring to from an electrical circuit. Neglect the resistance of the ring and the rod. Initially, the switch is open. (a) What is the induced emf across the terminals of the switch? (b) The switch S is closed at time t = 0 (i) Obtain an expression for the current as a function of time. (ii) In the steady state, obtain the time dependence of the torque, rod OA was along the positive X– axis at t = 0. Q.46. XY is an infinite current carrying wire carrying a current I. AB is a conducting rod of length L rotating about its centre O with an angular velocity ‘’. At the instant shown it is perpendicular to the wire XY and end B is at a distance ‘d’ from wire XY. Calculate the emf induced between centre O and point B at this instant (vB – v 0 = ?)
X
Y
I d B
L O
A
Q.47. In the adjoining diagram, a current-carrying loop pqrs is placed with its sides parallel to a long current-carrying wire. The currents i1 and i2 in the wire and loop are 20 A and 16 A respectively. If a = 15 cm, b = 6 cm and d = 4 cm, what will be the force on current-loop pqrs? What will be the difference in the force, if the current i2 in the loop is clockwise instead of anticlockwise?
i1 q
p
a
i2
s d
r b
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