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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 EngineeringLevel 1 Term 1

Session 1999-2000

Partners Roll No. 9906112

9906113

9906115

9906116

Date of Performance:Date of Submission:

Bangladesh University of Engineering and

TechnologyOBJECTIVE:

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This experiment is intended to verify Kirchhoffs Voltage Law (KVL) and voltagedivider 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 thanohms law are applied in order to find the current flowing in the various branches.These laws, discovered by the German physicist Gustav Robert Kirchhoff, areknown as Kirchhoff's laws of networks. The first of Kirchhoff's laws is known asKCL, And the second law which is known as KVL states that, starting at anypoint in a circuit and following any closed path back to the starting point, the netsum of the electromotive forces encountered will be equal to the net sum of theproducts 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 risesequals the algebraic sum of the voltage drops.

= VdropsVrises

The Voltage Divider rule is given by

Vx =Rs

Rx Vs

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

== RxRs R1+R2+R3

APPARATUS:

One DC Voltmeter (0-300V)

One DC Ammeter (0-5A) Two Rheostats One SPST switches

One multi meter DC power supply

PROCEDURE:

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Three rheostats R1 and R2 in series was connected through a SPST switch toa DC power supply as shown in fig. 1.

30V DC from DC power supply was applied.

Then the rheostats was set at their maximum value and readings of V1, V2, Vwas taken using a voltmeter.

Reading of Current or I was taken using an ammeter. Then the rheostatswere varied in such a way that the ammeter reading does not exceed thecurrent 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 =

RxRs =R1+R2+R3.

It was compared then withexperimentally obtained value Req=Vs/I. And for each set of data voltagedivider was verified.

TABLE:

ObservationNo.

VsVolts

IAmps

V1Volts

V2Volts

= RxRo

=R1+R2+R3

Rs=Vs/I

Ohms

V=V1+V2+V3

1 177 0.126 49.5 117 1321.43 1404.76 166.5

2 177 0.183 111 61 939.89 967.21 1723 175.5 0.2085 141 28.5 812.95 839.21 169.5

4 174 0.32 90 88 556.25 543.75 1785 174 0.385 55 117 446.75 451.95 172

CALCULATION:

AV1

V2

R1

R2Req

V +--

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We know that, R= V/I

For observation 1: (Sample)

R1 = V1/I = 49.5/0.126 = 392.86 R2 = V2/I = 117/0.126 = 928.57

Ro = R1+R2 = 1321.43

76.1404126.0

177===

I

VsRs

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 aseries combination with the whole circuit. Vs is obtained by the indicator of theconstant power source. Confirmation was made of Vs by measuring the voltageof the power source with a voltmeter. The summation of the resistance of therheostats was Ro.

And the division of Vs by I was Rs. The potential difference of each rheostats wasmeasured 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 errorcant be omitted. So whenever we obtained a reading by a meter we get a leasterror. These error is summed up after any calculation that was performed withthese readings. As the least error of reading of a multi meter is different from theleast error of the ammeter or voltmeter which is also different. So, whenever wedivide the Vs by I we get a little difference result from summating the individualresistance of the rheostats.

Loading effect of the meter: A voltmeter has a infinite resistance and anammeter 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 verysmall one. So whenever an ammeter is placed in the circuit, the equivalentresistance differs slightly & the total current of the circuit with an ammeter alsodiffers for this. Again whenever a voltmeter is placed to obtained the voltage thevoltage differs from the voltage of the rheostats without a voltmeter connected inparallel.

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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 aresistor of which potential difference needed to be measured and they arearranged in a parallel combination. In a circuit, an ammeter is used in aseries combination with a resistor of whose current that passes through ofthe resistor to be measured.

2. If an ammeter is connected in parallel across an element what could bethe possible danger.

If an ammeter us connected in parallel across an element then there arefollowing chances of dangers. As ammeter measures current across an element so its resistance is

near about zero. So, there occurs an short circuit, and almost all of thecurrents pass through the ammeter. So, all other elements of that circuitbecame 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 energyjustifythe statement.

As all the elements are in series.So,Vs=V1+V2And P=VI

I

PV =

tQ

tEV

/

/=

Q

E

V =

Q

E

Q

EVs 21 +=

Q

E

Q

E

Q

ES 21

+=

21 EEES +=

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

When,V = VoltageP = PowerE = EnergyQ = ChargeI = Currentt = Time

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Justified.

4. Why rheostats have current ratings in addition to resistance rating?

Current produce heat in accordance with the formula H = R.I2 . and particularresistor has a particular melting point. If the specific heat of the resistor be Sand produced temperature be t and the mass of the resistor be m then theformula is, H= m.S.t.Hence,

m.S.t = RI2t = 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 thecurrent exceeds such a way that regarding temperature exceeds its meltingpoint then it will be melted and go out of order. So the rheostats have currentrating as well as resistance rating so that we can control the limit of currentthat passes through it by controlling the potential difference of the two pointsof it.

5. KVL is applicable for open circuit tooverify.

KVL states that around any closed circuit the algebraic sum of the voltagerises 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 terminalsand thus the total arrangement is a loop. As it is an open circuit, there is nocurrent passing through it. So I is 0.

VI = R.I = R.0 = 0 -----------------------(1)

Suppose, for the open terminal, potential difference is Vopen. And the sign ofvoltage is according to the figure. Then, applying Kirchoffs voltage law to thecircuit, we get,

+ Vo V Vopen = 0 ; + Vo Vopen = 0; [since according to the equation 1 V=0] Vo = Vopen

VopenVo

R

V

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So there is a opposite and equal voltage to the battery in the open terminalthat force the battery not to pass current through the circuit. Thus the

Kirchoffs Voltage law is applicable to an open circuit, too.

DISCUSSION:

To analyze a complex electric circuits KVL is a must. Because it bearsimplication for analyzing a particular loop of a complex circuit. So, it is reallyimportant to learn how to apply KVL to a simple circuit. So, the verification ofKVL make us a bit skillful to design a complex circuit. In the practical field, theidea 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 touse those sophisticated Electrical Elements.