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EXPERIMENT 9
SUPERPOSITION THEOREM
OBJECTIVES:
To study and apply the Superposition theorem in the solution of an
electric circuit.
DISCUSSION:
The Superposition theorem may be stated as follows. The current which
flows at any point in the network involving more than one source may be
considered to be the algebraic sum of the currents which flows as a result of
each source taken separately.
In taking each source separately, the other sources like batteries are
replaced with a short circuit and current sources are replaced with an open
circuit.
Consider the circuit shown in Fig 9.1. To apply the Superposition theorem
to such a circuit, we first replaced the EB source with a short circuit as shown
in Fig 9.2a. I1A, I2A and I3A are computed using Ohm’s law. Then we return source
EB and remove source EA replacing it with a short circuit. I1B, I2B and I3B are then
determined using Ohm’s law.
We may now combine the results of the two sets of calculation to find the
currents I1, I2 and I3 in Fig 9.1. We observe in this case that I1A and I1B oppose
each other, as do I2A and I2B. on the other hand, I3A and I3B reinforce each other.
Consequently, we hence
I1 = I1A – I1B
,
I2 = I2A – I2B
,
I3 = I3A + I3B
The directions in which I1, I2 and I3 will flow are determined by the
directions of the component currents. That is, in the case of I1, the direction will
be the same as the larger if I1A and I1B. the same is true with I2 with respect to
I2A and I2B. for I3, it will be in the same direction as I3A and I3B.
INSTRUMENT AND COMPONENTS:
VOM
DC Voltmeter
DC Ammeter
250-ohm resistor
100-ohm resistor
75-ohm resistor
50-ohm resistor
DC Power Supply
Connecting Wires
PROCEDURE:
1. Connect the circuit shown in Fig 9.1. The values of the resistors
and voltages of the sources will be assigned by your instructor.
2. Measure and record each of the currents I1, I2 and I3.
3. Disconnect the EB source and place a short-circuiting wire across
the network between points B and B’.
4. Measure and record the current I1A, I2A and I3A.
5. Remove the short-circuiting wire and reconnect the EB source.
Remove EA source and place a short-circuiting wire in place.
6. Measure and record the current I1B, I2B and I3B.
7. Compute for I1’, I2’ and I3’ using the measured component
currents.
8. Compute the percent difference between each of the pairs of values
of I1, I2 and I3
EXPERIMENTAL SET-UP
CIRCUITS DIAGRAMS
Fig. 9.1 Experimental Circuit
Fig. 9.2 Experimental Circuit
DATA AND RESULTS:
I1
I2
I3
COMPUTATIONS:
I1A
I2A
I3A
I1B
I2B
I3B
I1’
I2 ’
I3’
PROBLEMS:
1. What happens to the terminal voltage of a Norton’s equivalent circuit when
a load resistor is connected to it?
2. What is the difference between a Thevenin’s equivalent circuit and a
Norton’s equivalent circuit?
CONCLUSION: