Circuit Theorems

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EGR 2402 Laboratory Manual

22

Experiment # 04


Circuit Theorems


Object:




Illustrate the superposition theorem.



Thevenin’s and Norton's theorem.



Reciprocity theorem for linear circuits


Apparatus:




Dual DC power supply (0
-
20V).



Multimeter.



Ohmmeter.



Three
-
port resistor network.



Circ
uit board.



Different resistors.


Experimental set
-
up and procedure
:


I. Two
-
port resistor network


Consider a two
-
port resistor network as in Fig. 1.









Fig.1


1. Set up the circuit in Fig. 1.

2. Connect port 1 to a DC powe
r supply (voltage source).

3. What is Thevenin's, and Norton's theorems?

4. Calculate the Thevenin and Norton equivalents of this circuit.

5. Take the necessary measurements to determine the Thevenin and Norton equivalents of this circuit.

6. Explain w
hy you took such measurements.

7. Give the % errors on the measured values.


I
-
Three
-
port resistor network


Consider the 3
-
port resistor network shown in Fig. 2.











Fig.2


a) Superposition theorem

1.

Apply different voltages V
2

at
port 1 and simultaneously apply V
3
at port 3

2.

Measure the short circuit current I
sc

at port 1 and record your values in Table 1





2

1

R
2

R
4

R
1

R
3

2

1

3

EGR 2402 Laboratory Manual

23

3. Disconnect the power supply from port 2

4. Measure the current I
2
at port 1 when port 2 is shorted out for the differen
ce values of V
3

5. Disconnect the power supply from port 3

6. Measure the current I
3

at port 1 when port 3 is shorted out for the different values of V
2


7. Calculate the % error on I
sc
and record all your values in Table 1:



V2 (Volts)

V3 (Volts)

I
2

I
3

I
2
+I
3

I
sc

% Error

2

3






4

5






6

15






15

6






20

2







8. What is the superposition theorem?

9. Does it hold in this case? Explain


b) Thevenin and Norton theorems

1.

Connect a DC power supply to port 1 and apply a voltage V
1

= 10V

2.

Short
-
circuit the terminals in port 3

3.

At port 2, measure the open circuit voltage V
2

and the short
-
circuit current I
2

4.

Find the Thevenin and Norton parameters for port 2

5.

Disconnect the power supply from port 1

6.

Connect to port 1 a resistance equal to the power

supply internal resistance

7.

Measure the total resistance R
T

of the circuit at port 2

8.

Compare R
T
to the Thevenin resistance R
Th

and give the % error

9.

Complete Table II:


V
1

(Volts)

V
2

1
2

R
T

R
Th

% error

10








10. Does Thevenin's and Norton's th
eorems hold? Explain


c) The reciprocity theorem

1. Place the DC power supply at port 1 and apply different voltages U.

2. Short circuit the terminals at port 3

3. Connect an ammeter to port 2 and measure the current I
2


4. Interchange the voltage sourc
e and the ammeter and measure I
l


5. Compare I
2
to I
1

and give the % difference

6. Record your measurements in Table III :


U (Volts)

I1

I2

% Difference

2




5




10




15




20





7. What is the reciprocity theorem?

8. Is

this theorem obeyed he
re? Explain?

9. What could be the main origin of the calculated % difference?

Conclusion:


1. What did you learn from these experiments? Explain and give some applications?

3.

What could we place inside the three
-
port networks to make it not satisfy some o
f these circuit
theorems? Explain ?





EGR 2402 Laboratory Manual

24

Experiment # 04

Name:

Section:


Circuit Theorems


I.

Two
-
port resistor network


5. Thevenin and Norton parameters


II.
Three
-
port resistor network


a) Superposition theorems



V2(volts)

V3 (Volts)

I
2

I
3

I
2
+I
3

% E
rror

2

3





4

5





6

15





15

6





20

2







b) Thevnin and Norton theorems


V
1
(Volts)


V
2

I
2

RT

R
th

% Error











c)
The

reciprocity theorem:



U (Volts)

I
1

I
2

% Difference

2




5




10




15




20