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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: