Laboratory Material

LABORATORY MATERIAL

EE0211 – ELECTRICAL CIRCUITS LAB

CONTENTS

Sl.No. / Name of the Experiments / Page No.
1 / Verification of Kirchoff’s laws / 3
2 / Verification of Superposition theorem / 6
3 / Verification of Thevenin’s & Norton’s Theorem / 9
4 / Verification of Maximum Power Transfer theorem / 15
5 / Power measurement in 3 phase unbalanced circuits / 19
6 / Power measurement in 3 phase balanced circuits / 20
7 / Power measurement using 3 voltmeter & 3 ammeter / 22
method
8 / Circuit analysis using CRO / 26
9 / Circuit transients by digital simulation / 28
10 / Study of resonance / 30

Experiment No. 1 / VERIFICATION OF KIRCHHOFFS LAWS
Date :

Aim:

To verify Kirchhoff’s current law and Kirchhoff’s voltage law for the given circuit.

Apparatus Required:

Sl.No. / Apparatus / Range / Quantity
1 / RPS (regulated power supply) / (0-30V) / 2
2 / Resistance / 330, 220 1k / 6
3 / Ammeter / (0-30mA)MC / 3
4 / Voltmeter / (0-30V)MC / 3
5 / Bread Board & Wires / -- / Required

Statement:

KCL: The algebraic sum of the currents meeting at a node is equal to zero. KVL: In any closed path / mesh, the algebraic sum of all the voltages is zero.

Precautions:

Voltage control knob should be kept at minimum position.
Current control knob of RPS should be kept at maximum position.

Procedure for KCL:

Give the connections as per the circuit diagram.
Set a particular value in RPS.
Note down the corresponding ammeter reading
Repeat the same for different voltages

Procedure for KVL:

Give the connections as per the circuit diagram.
Set a particular value in RPS.
Note all the voltage reading
Repeat the same for different voltages

Circuit - KCL

Circuit - KVL

KCL - Theoretical Values:

Sl. / Voltage / Current / I1 = I2 + I3
No. / E / I1 / I2 / I3
Volts / mA / mA / mA / mA
1 / 5 / 5.68 / 3.12 / 2.56 / 5.68
2 / 10 / 11.3 / 6.18 / 5.12 / 11.3
3 / 15 / 17.05 / 9.37 / 7.68 / 17.05
4 / 20 / 22.73 / 12.49 / 10.24 / 22.075
5 / 25 / 28.42 / 15.62 / 12.68 / 28.42
KCL - Practical Values:
Sl. / Voltage / Current / I1 = I2 + I3
No. / E / I1 / I2 / I3
Volts / mA / mA / mA / mA
1 / 5 / 5.6 / 3.1 / 2.2 / 5.3
2 / 15 / 17.2 / 9.4 / 7.6 / 17
3 / 25 / 28 / 15.6 / 12.7 / 28.3

KVL – Theoretical Values

Sl.No. / RPS / Voltage / KVL
E1 / E2 / V1 / V2 / V3 / E1 = V1 + V2
V / V / V / V / V / V
1 / 5 / 5 / 0.58 / 4.41 / 0.583 / 4.99
2 / 10 / 10 / 1.16 / 8.83 / 1.17 / 9.99
3 / 15 / 15 / 1.75 / 13.2 / 1.75 / 14.95
4 / 20 / 20 / 2.33 / 17.67 / 2.33 / 20
5 / 25 / 25 / 2.913 / 22.08 / 2.915 / 24.993

KVL - Practical Values

Sl.No. / RPS / Voltage / KVL
E1 / E2 / V1 / V2 / V3 / E1 = V1 + V2
V / V / V / V / V / V
1 / 5 / 5 / 0.6 / 4.4 / 0.56 / 5
2 / 10 / 10 / 1.13 / 8.83 / 1.19 / 9.96
3 / 15 / 15 / 1.72 / 13.20 / 1.78 / 14.92

Model Calculations:

Result:

Thus Kirchoff’s voltage load and Kirchoff’s current law verified both theoretically and practically.

Experiment No. 2 / VERIFICATION OF SUPERPOSITION THEOREM
Date :

Aim:

To verify the superposition theorem for the given circuit.

Apparatus Required:

Sl.No. / Apparatus / Range / Quantity
1 / RPS (regulated power supply) / (0-30V) / 2
2 / Ammeter / (0-10mA) / 1
3 / Resistors / 1k, 330, 220 / 3
4 / Bread Board / -- / --
5 / Wires / -- / Required

Statement:

Superposition theorem states that in a linear bilateral network containing more than one source, the current flowing through the branch is the algebraic sum of the current flowing through that branch when sources are considered one at a time and replacing other sources by their respective internal resistances.

Precautions:

Voltage control knob should be kept at manimum position
current control knob of RPS should be kept at maximum position

Procedure:

Give the connections as per the diagram.
Set a particular voltage value using RPS1 and RPS2 & note down the ammeter reading

Set the same voltage in circuit I using RPS1 alone and short circuit the terminals and note the ammeter reading.

Set the same voltage in RPS2 alone as in circuit I and note down the ammeter reading.

Verify superposition theorem.

CIRCUIT - 1

CIRCUIT - 2

CIRCUIT - 3

TABULAR COLUMN

Theoretical Values

RPS / Ammeter Reading (I)
1 / 2 / mA
Circuit – 1 / 10 V / 10 V / I = 8.83
Circuit – 2 / 10 V / 0 V / I’= 3.5
Circuit – 3 / 0 V / 10 V / I”= 5.3
I = / I’  I” = 8.83
Practical Values
RPS / Ammeter Reading (I)
1 / 2 / mA
Circuit – 1 / 10 V / 10 V / I = 8.5
Circuit – 2 / 10 V / 0 V / I’= 3.5
Circuit – 3 / 0 V / 10 V / I”= 5
I = / I’  I” = 8.5 mA
= 3.5 + 5 = 8.5 mA

Model Calculations:

Result:

Superposition theorem have been verified theoretically and practically.

Experiment No. 3 / VERIFICATION OF THEVENIN’S THEOREM
Date :

Aim:

To verify Thevenin’s theorem and to find the full load current for the given circuit.

Apparatus Required:

Sl.No. / Apparatus / Range / Quantity
1 / RPS (regulated power supply) / (0-30V) / 2
2 / Ammeter / (0-10mA) / 1
3 / Resistors / 1K, 330 / 3,1
4 / Bread Board / -- / Required
5 / DRB / -- / 1

Statement:

Any linear bilateral, active two terminal network can be replaced by a equivalent voltage source (VTH). Thevenin’s voltage or VOC in series with looking pack resistance RTH.

Precautions:

Voltage control knob of RPS should be kept at minimum position.
Current control knob of RPS should be kept at maximum position

Procedure:

Connections are given as per the circuit diagram.

Set a particular value of voltage using RPS and note down the corresponding ammeter readings.

To find VTH

Remove the load resistance and measure the open circuit voltage using multimeter (VTH).

To find RTH

To find the Thevenin’s resistance, remove the RPS and short circuit it and find the

RTH using multimeter.

Give the connections for equivalent circuit and set VTH and RTH and note the corresponding ammeter reading.
Verify Thevenins theorem.

Theoretical and Practical Values

E(V) / VTH(V) / RTH() / IL (mA)
Circuit - I / Equivalent
Circuit
Theoretical / 10 / 5 / 495 / 3.34 / 3.34
Practical / 10 / 4.99 / 484 / 3.3 / 3.36

Circuit - 1 : To find load current

To find VTH

To find RTH

Thevenin’s Equivalent circuit:

Model Calculations:

Result:

Hence the Thevenin’s theorem is verified both practically and theoretically

Experiment No. 4 / VERIFICATION OF NORTON’S THEOREM
Date :

Aim:

To verify Norton’s theorem for the given circuit.

Apparatus Required:

Sl.No. / Apparatus / Range / Quantity
1 / Ammeter / (0-10mA) MC / 1
(0-30mA) MC / 1
2 / Resistors / 330, 1K / 3,1
3 / RPS / (0-30V) / 2
4 / Bread Board / -- / 1
5 / Wires / -- / Required

Statement:

Any linear, bilateral, active two terminal network can be replaced by an equivalent current source (IN) in parallel with Norton’s resistance (RN)

Precautions:

Voltage control knob of RPS should be kept at minimum position.
Current control knob of RPS should be kept at maximum position.

Procedure:

Connections are given as per circuit diagram.

Set a particular value in RPS and note down the ammeter readings in the original circuit.

To Find IN:

Remove the load resistance and short circuit the terminals.
For the same RPS voltage note down the ammeter readings.

To Find RN:

Remove RPS and short circuit the terminal and remove the load and note down the resistance across the two terminals.

Equivalent Circuit:

Set IN and RN and note down the ammeter readings.

Verify Norton’s theorem.

To find load current in circuit 1:

To find IN

To find RN

Norton’s equivalent circuit

Constant current source

Theoretical and Practical Values

E / IN / RN / IL (mA)
(volts) / (mA) / ()
Circuit - I / Equivalent
Circuit
Theoretical / 10 / 10.10 / 495 / 334 / 3.34
Values
Practical / 10 / 10.4 / 485 / 3.4 / 4
Values

Model Calculations:

Result:

Norton’s was verified practically and theoretically

Experiment No. 5 / VERIFICATION OF MAXIMUM POWER TRANSFER
Date : / THEOREM

Aim:

To verify maximum power transfer theorem for the given circuit

Apparatus Required:

Sl.No. / Apparatus / Range / Quantity
1 / RPS / (0-30V) / 1
2 / Voltmeter / (0-10V) MC / 1
3 / Resistor / 1K, 1.3K, 3 / 3
4 / DRB / -- / 1
5 / Bread Board & wires / -- / Required

Statement:

In a linear, bilateral circuit the maximum power will be transferred to the load when load resistance is equal to source resistance.

Precautions:

Voltage control knob of RPS should be kept at minimum position.

Current control knob of RPS should be kept at maximum position.

Procedure:

Circuit – I

Connections are given as per the diagram and set a particular voltage in RPS.
Vary RL and note down the corresponding ammeter and voltmeter reading.

Repeat the procedure for different values of RL & Tabulate it.
Calculate the power for each value of RL.

To find VTH:

Remove the load, and determine the open circuit voltage using multimeter (VTH)

To find RTH:

Remove the load and short circuit the voltage source (RPS).
Find the looking back resistance (RTH) using multimeter.

Equivalent Circuit:

Set VTH using RPS and RTH using DRB and note down the ammeter reading.

Calculate the power delivered to the load (RL = RTH)
Verify maximum transfer theorem.

Circuit - 1

To find VTH

To find RTH

Thevenin’s Equation Circuit

Power VS RL

Circuit – I

Sl.No. / RL () / I (mA) / V(V) / P=VI (watts)
1 / 200 / 1.3 / 0.27 / 0.26
2 / 400 / 1.2 / 0.481 / 0.53
3 / 600 / 1.1 / 0.638 / 0.707
4 / 800 / 1 / 0.771 / 0.771
5 / 1200 / 0.80 / 1.083 / 0.866
6 / 1300 / 0.77 / 1.024 / 0.788
7 / 1400 / 0.74 / 0.998 / 0.738
8 / 1500 / 0.71 / 0.968 / 0.687
To find Thevenin’s equivalent circuit
VTH (V) / RTH () / IL (mA) / P (milli watts)
Theoretical / 2002 / 1320 / 0.758 / 0.759
Value
2 / 1306 / 0.77 / 0.77
Practical Value

Model Calculations:

Result:

Thus maximum power theorem was verified both practically and theoretically

Experiment No. 6 / THREE PHASE POWER MEASUREMENT
Date : / (TWO WATTMETER METHOD)

Aim:

To measure the 3-phase active and reactive power by 2 – wattmeter method for (i) resistance load (ii) inductive load

Apparatus Required:

Sl.No. / Apparatus / Range / Quantity
1 / Voltmeter / (0-600V) MI / 1
2 / Ammeter / (0-20A) MI / 1
3 / Wattmeter / 600V, 10A, UPF / 2
4 / Wattmeter / 600V, 10A, LPF / 2

Precautions:

THE TPST switch must be kept open initially.

Load must not be applied while starting.

Procedure:

(i) – Resistive load

Give the connections as per the circuit diagram.
Give the supply by closing TPST switch.
Vary the resistance load and note down the corresponding readings.

(ii)Inductive load

Give the connections as per the circuit diagram.
Give the supply by closing the TPST switch
Vary the inductive load and note down the corresponding readings.

for inductive load

for resistive load

Formulae Used:

1.Real power = w1 + w2

2.Reactive power = 3(w1w2 )

3.Tan= 3(w1w2)

w1 w2

Power factor = cos 

Two Wattmeter Method : Resistive Load

MF = / MF = / Power
V / I / Wattmeter / Wattmeter
(volt) / (A) / Reading (W1) / Reading (W2) / Cos 
OBS / ACT = / OBS / ACT=OBS / Real / Reactive
(watt) / OBS X / (watt) / x MF / Power / power
MF / (watt) / (watt) / (watt)
(watt)
460 / 0 / 0 / 0 / 0 / 0 / 0 / 0 / 0
460 / 1.8 / 70 / 560 / 90 / 720 / 1280 / -277.12 / 0.977
460 / 3.7 / 160 / 1280 / 180 / 1440 / 2720 / -277.12 / 0.9949
460 / 4.6 / 200 / 1600 / 210 / 1680 / 3280 / -138.56 / 0.999
460 / 5.5 / 240 / 1920 / 250 / 2000 / 3920 / -138.56 / 0.9
460 / 6.3 / 280 / 2240 / 290 / 2320 / 4560 / -138.56 / 0.993
460 / 7.2 / 320 / 2560 / 330 / 2640 / 5200 / -138.56 / 0.996
460 / 8.1 / 350 / 2800 / 370 / 2960 / 5760 / -277.12 / 0.9988
460 / 9 / 390 / 3120 / 410 / 3280 / 6400 / -277.12 / 0.990
20

Two Wattmeter Method : Inductive Load

MF = / MF = / Power
Wattmeter / Wattmeter
V / I / Reading (W1) / Reading (W2) / Cos 
(volt) / (A) / OBS / ACT = / OBS / ACT=OBS / Real / Reactive
(watt) / OBS x / (watt) / x MF / Power / power
MF / (watt) / (watt) / (watt)
(watt)
410 / 1 / 11 / 89 / 26 / 208 / 296 / -554.26 / 0.351
410 / 2 / 15 / 120 / 32 / 256 / 376 / -443.41 / 0.647
410 / 3 / 28 / 140 / 53 / 424 / 564 / -734.39 / 0.609
410 / 4 / 43 / 344 / 80 / 640 / 984 / -1108.51 / 0.664
410 / 5 / 78 / 624 / 106 / 848 / 1472 / -1461.78 / 0.708
410 / 6 / 95 / 760 / 132 / 1056 / 1816 / -1829.05 / 0.705

Model Calculations:

Result:

Thus power for three phase power supply was measured using 2 wattmeter method.

Experiment No. 7 / POWER MEASUREMENT BY 3 - VOLTMETER
Date :

Aim:

To measure the power in an inductive circuit, Eg: transformer, by 3- voltmeter method.

Apparatus Required:

Sl.No. / Apparatus / Range / Quantity
1 / Ammeter / (0-5A) MI / 1
2 / Voltmeter / (0-150V) MI / 2
(0-300V) MI / 1
3 / Transformer / 230V/115V, 1KVA / 1
4 / Auto Transformer / - / -
5 / Auto Transformer / - / 1
6 / Rheostat / 100 / 1

Precaution:

The DPST switch must be kept open initially.
The auto transformer must be kept at minimum potential position
The rheostat must be kept at maximum resistance position.

Procedure:

Give the connections as per the circuit diagram.
Adjust the auto transformer, to bring the rated voltage of the transformer
Note down the transformer and voltmeter readings.

Vary the rheostat for different values and note down the corresponding meter readings.

3 – Voltmeter Method

Sl. / I / Vs / VR / VL / P / Cos 
No. / (amp) / (volts) / (volts) / (volts) / (watts)
1 / 0.2 / 150 / 15 / 136 / 25.193 / 0.82
2 / 0.6 / 150 / 54 / 120 / 21.99 / 0.293
3 / 0.8 / 150 / 73 / 120 / 15.18 / 0.158
4 / 1 / 150 / 86 / 110 / 17.46 / 0.158
5 / 1.1 / 150 / 90 / 105 / 20.625 / 0.178
6 / 1.2 / 150 / 95 / 100 / 21.99 / 0.182

Formulae Used:
V 2 / V 2 / V 2
1. / Power (P) = / S / R / L / watts
2R
R = VR / I
Cos  = / V 2 / V / 2 / V / 2
2. / S / R / L
2 Ve / VL

Model Calculations:

Result:

The power was measured for given circuit using 3 voltmeter method

Experiment No. 8 / POWER MEASUREMENT BY 3 - AMMETER
Date :

Aim:

To measure the power in an inductive circuit, Eg: transformer, by 3- ammeter method.

Apparatus Required:

Sl.No. / Apparatus / Range / Quantity
1 / Ammeter / (0-2A) MI / 2
(0-5A) MI / 1
2 / Voltmeter / (0-150V) MI / 1
3 / Auto transformer / - / 1
4 / Transformer / 230V/115V / 1
1KVA, 1
5 / Rheostat / 100 / 4A / 1

Precaution

The DPST switch must be kept open initially
The autotransformer should be kept at minimum potential position
The rheostat should be kept at maximum resistance position

Procedure:

Give the connections as per the circuit diagram
Adjust the auto transformer, to bring the rated voltage of the transformer
Note down the ammeter and voltmeter readings.
Vary the rheostat for different values and note

3 – Voltmeter Method

Sl. / V / Is / IR / IL / R / P / Cos 
No. / (volts) / (amp) / (amp) / (amp) / (ohm) / (watts)
1 / 115 / 0.75 / 0.54 / 0.48 / 213 / 4.31 / 0.07
2 / 115 / 0.85 / 0.6 / 0.48 / 191.67 / 912.6 / 0.22
6 / 115 / 0.95 / 0.7 / 0.48 / 164.3 / 14.9 / 0.57
4 / 115 / 1.05 / 0.8 / 0.48 / 143.7 / 16.6 / 0.3
5 / 115 / 1.15 / 0.9 / 0.48 / 127.7 / 18 / 0.32
6 / 115 / 1.25 / 1 / 0.46 / 0.46 / 20.1 / 0.37

Formulae Used:
Power (P) = / R / I S2  I R2 /  I L2 / 
2
R = V / IR
Power factor cos  = / I / 2 /  I 2 /  I 2
S / R / L
2 IR / I L

Model Calculations:

Result:

Thus power was measured using 3 ammeter method

Experiment No. 9 / CIRCUIT ANALYSIS USING CRO
Date :

Aim:

To measure voltage and current and also to study the phase relationship between supply voltage and current in series RC circuit.

Apparatus Required:

Sl.No. / Apparatus / Range / Quantity
1 / Function generator / 1
2 / DMM / 1
3 / Resistor / 200  / 1
4 / Capacitor / 1 F / 1
5 / CRO / 1

Procedure:

Connections are given as per the circuit diagram.

In the function generator, select “SINE WAVE” as the output and set the frequency to 200 Hz.

Adjust the amplitude knob of the function generator until the waveform on the oscilloscope shows 2 Vp.

Record the peak voltage across the resistor using CRO.

Calculate  from t.
Draw the waveform for VS, VR.

Circuit Diagram:

Sl.No. / Frequency / VR / T / t / 
(Hz) / V / (ms) / (ms) / deg
1 / 200 / 0.4 / 5 / 0.3 / 21.6

(leading

Sl.No. / Frequency / VR / T / t / 
(Hz) / V / (ms) / (ms) / deg
1 / 0.32 / 1.6mA / 1.2 / 750 / 7.95

Result:

The phase relationship between supply voltage and current in series RC circuit is studied and also the voltage and current are increased practically.

Experiment No. 10 / CIRCUIT TRANSIENTS BY SIMULATION IN RL
Date : / CIRCUIT

Aim:

To simulate the RL circuit using Pspice software and to study the transient response

Circuit Diagram:

Simulation Parameter:

Vdc = 10 volts, R1 = 50 ohms, L = 100mH

Simulation Output:

Transient L wave form

Transient R wave form

Result:

Simulation of the RL transient circuit was done

Experiment No. 11 / STUDY OF RESOURCE
Date :

Aim:

To study series and parallel resource in AC circuit

Series Resource:

An RLC circuit is said to be at re source when voltage and current are in phase with each other and power factor is unity.

Z R  j( X L  X C)z

At series resource / XL = XC
Z = R
XL = XC
 /  / 1
L / C
2 /  / 1
L
C
(2 / fr )2  / 1
n / LC
f r /  / 1
2 / LC
Power factor cos / R
Z
Q - factor = / VC /  / VL
V / V

Parallel Resonance:

Parallel AC circuit is said to be at resource when voltage and current are in phase with each other and power factor is unity.

(i) / ideal parallel circuit / f 0 /  / 1
2u / LC
(ii) / Practical circuit - I f /  / 1 / 1 /  / R 2
0 / L2
2 / L
u
C
 / 
1 / (RL )2 /  L / C
(iii) / Practical circuit – II / f0 /  /  / 
2 / u / I / C /  / (R / L / )2 /  L / C 
 / 