Eee 02

Name of the Experiment: VERIFICATION OF KVL & VOLTAGE DEVIDER RULE

Course No. EEE 102 Experiment No. 2 Group No. 2

Mursalin Habib Roll No. 9906114 Department: Electrical and Electronics Engineering Level 1 Term 1 Session 1999-2000 Partners Roll No.

9906112 9906113 9906115 9906116

Date of Performance: Date of Submission:

Bangladesh University of Engineering and Technology OBJECTIVE: 

This experiment is intended to verify Kirchhoff’s Voltage Law (KVL) and voltage divider rule with the help of series circuits and hence derive equivalent resistance both experimentally and analytically.

THEORY: 

If a circuit has a number of interconnected branches, two other laws other than ohms law are applied in order to find the current flowing in the various branches. These laws, discovered by the German physicist Gustav Robert Kirchhoff, are known as Kirchhoff's laws of networks. The first of Kirchhoff's laws is known as KCL, And the second law which is known as KVL states that, starting at any point in a circuit and following any closed path back to the starting point, the net sum of the electromotive forces encountered will be equal to the net sum of the products of the resistance encountered and the currents flowing through them. Or Simply, KVL states that around any closed circuit the algebraic sum of the voltage rises equals the algebraic sum of the voltage drops.

∑Vrises = ∑ Vdrops The Voltage Divider rule is given by Vx =

 Rx  Rs

× Vs

The equivalent (total) resistance of a series circuit is given by  Rs

=

  3  ∑ Rx = R 1+R 2+R 

APPARATUS:  • • • • • •

One DC Voltmeter (0-300V) One DC Ammeter (0-5A) Two Rheostats One SPST switches One multi meter DC power supply

PROCEDURE: 

• •

Three rheostats R1 and R2 in series was connected through a SPST switch to a DC power supply as shown in fig. 1. 30V DC from DC power supply was applied.

R1 A V

V1

+ --

V2

Req • •

• •

R2

Then the rheostats was set at their maximum value and readings of V 1, V2, V was taken using a voltmeter. Reading of Current or I was taken using an ammeter. Then the rheostats were varied in such a way that the ammeter reading does not exceed the current rating of any of the rheostats. Whole Process was repeated for 5 times. KVL was verified with all the Data was taken. Total resistance of the series circuit was calculated using  Rs = ∑ Rx =R 1+R 2 +R 3. It was compared then with experimentally obtained value R eq=Vs /I. And for each set of data voltage divider was verified.

TABLE: 

Observation No.

Vs Volts

I Amps

V1 Volts

V2 Volts

1 2 3 4 5

177 177 175.5 174 174

0.126 0.183 0.2085 0.32 0.385

49.5 111 141 90 55

117 61 28.5 88 117

CALCULATION: 

R 3 

Rs= Vs /I Ohms

V=V1+V2 +V3

1321.43 939.89 812.95 556.25 446.75

1404.76 967.21 839.21 543.75 451.95

166.5 172 169.5 178 172

 Ro = ∑ Rx

=R  +R  +  1

2 

We know that, R= V/I For observation 1: (Sample) R1 = V1 /I = 49.5/0.126 = 392.86 Ω R2 = V2 /I = 117/0.126 = 928.57 Ω Ro = R1+R2 = 1321.43  Rs

=

Vs  I 

=

177 0.126

Ω

= 1404.76 Ω

REPORT:  Comment on the result obtained and discrepancies. (If any)

Results obtained: For each observation, the current, ‘I’ is obtained by placing an ammeter in a series combination with the whole circuit. V s is obtained by the indicator of the constant power source. Confirmation was made of V s by measuring the voltage of the power source with a voltmeter. The summation of the resistance of the rheostats was Ro. And the division of V s by I was Rs. The potential difference of each rheostats was measured by a voltmeter placing in parallel combination of each rheostat. Discrepancies:

There is two reasons for discrepancies.

Reading error: While the reading is obtained by a meter, at least parallax error can’t be omitted. So whenever we obtained a reading by a meter we get a least error. These error is summed up after any calculation that was performed with these readings. As the least error of reading of a multi meter is different from the least error of the ammeter or voltmeter which is also different. So, whenever we divide the Vs by I we get a little difference result from summating the individual resistance of the rheostats. Loading effect of the meter: A voltmeter has a infinite resistance and an ammeter has a resistance of zero – is theoretically true but not in practical use. Practically a voltmeter has a very big resistance and an ammeter has a very small one. So whenever an ammeter is placed in the circuit, the equivalent resistance differs slightly & the total current of the circuit with an ammeter also differs for this. Again whenever a voltmeter is placed to obtained the voltage the voltage differs from the voltage of the rheostats without a voltmeter connected in parallel.

QUESTIONS & ANSWER: 

1. State the rules of connecting voltmeter and ammeter in the circuit. In a circuit the two leads of a voltmeter is directly connected to points of a resistor of which potential difference needed to be measured and they are arranged in a parallel combination. In a circuit, an ammeter is used in a series combination with a resistor of whose current that passes through of the resistor to be measured.

2. If an ammeter is connected in parallel across an element what could be the possible danger. If an ammeter us connected in parallel across an element then there are following chances of dangers. • As ammeter measures current across an element so it’s resistance is near about zero. So, there occurs an short circuit, and almost all of the currents pass through the ammeter. So, all other elements of that circuit became invalid. • As most of the current pass through the ammeter so it may burn out. 3. “KVL is a restatement of the law of the conservation of energy”—justify the statement. As all the elements are in series. So,Vs=V1+V2 And P=VI  ⇒ V  = ⇒ V  = ⇒ V  =

P  I   E  / t  Q / t   E  Q

⇒ Vs = ⇒

 E S  Q

When, V = Voltage P = Power E = Energy Q = Charge I = Current t = Time

 E 1

=

Q

+

 E 1 Q

 E 2

+

Q  E 2 Q

⇒  E S  =  E 1 + E 2

So, “KVL is a restatement of the law of the conservation of energy”

Justified.

4. Why rheostats have current ratings in addition to resistance rating? Current produce heat in accordance with the formula H = R.I 2 . and particular resistor has a particular melting point. If the specific heat of the resistor be ‘S’ and produced temperature be ‘t’ and the mass of the resistor be ‘m’ then the formula is, H= m.S.t. Hence, m.S.t = RI2 t = RI2 / m.S So we can say that produced temperature is a function of current and it is directly proportional to the square of the current that passes through it. If the current exceeds such a way that regarding temperature exceeds its melting point then it will be melted and go out of order. So the rheostats have current rating as well as resistance rating so that we can control the limit of current that passes through it by controlling the potential difference of the two points of it.

5. “KVL is applicable for open circuit too”—verify. KVL states that around any closed circuit the algebraic sum of the voltage rises equals the algebraic sum of the voltage drops. So for the following open circuit, we can consider that, there a voltage exists in the two open terminals and thus the total arrangement is a loop. As it is an open circuit, there is no current passing through it. So ‘I’ is 0.

Vo

Vopen

V R

VI = R.I = R.0 = 0 -----------------------(1) Suppose, for the open terminal, potential difference is V open. And the sign of voltage is according to the figure. Then, applying Kirchoff’s voltage law to the circuit, we get, ⇒ + Vo – V – Vopen = 0 ; ⇒ + Vo – Vopen = 0; [since according to the equation 1 V=0] ⇒ Vo = Vopen

So there is a opposite and equal voltage to the battery in the open terminal that force the battery not to pass current through the circuit. Thus the Kirchoff’s Voltage law is applicable to an open circuit, too.

DISCUSSION: 

To analyze a complex electric circuits KVL is a must. Because it bears implication for analyzing a particular loop of a complex circuit. So, it is really important to learn how to apply KVL to a simple circuit. So, the verification of KVL make us a bit skillful to design a complex circuit. In the practical field, the idea of the results of the discrepancies makes us able to be alert of designing an electric circuit. An it was really encouraging for a freshman student like me to use those sophisticated Electrical Elements.