# 4.1.4: Procedure

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## 10.4.1: Voltage Application

1. Consider the dual supply circuit of Figure 10.3.1 using E1 = 10 volts, E2 = 15 volts, R1 = 4.7 k, R2 = 6.8 k and R3 = 10 k. To find the voltage from node A to ground, superposition may be used. Each source is considered by itself. First consider source E1 by assuming that E2 is replaced with its internal resistance (a short). Determine the voltage at node A using standard series-parallel techniques and record it in Table 10.5.1. Make sure to indicate the polarity. Repeat the process using E2 while shorting E1. Finally, sum these two voltages and record in Table 10.5.1.

2. To verify the superposition theorem, the process may be implemented directly by measuring the contributions. Build the circuit of Figure 10.3.1 with the values specified in step 1, however, replace E2 with a short. Do not simply place a shorting wire across source E2! This will overload the power supply.

3. Measure the voltage at node A and record in Table 10.5.1. Be sure to note the polarity.

4. Remove the shorting wire and insert source E2. Also, replace source E1 with a short. Measure the voltage at node A and record in Table 10.5.1. Be sure to note the polarity.

5. Remove the shorting wire and re-insert source E1. Both sources should now be in the circuit. Measure the voltage at node A and record in Table 10.5.1. Be sure to note the polarity. Determine and record the deviations between theory and experimental results.

## 10.4.2: Current and Power Application

6. Consider the dual supply circuit of Figure 10.3.2 using E1 = 10 volts, E2 = 15 volts, R1 = 4.7 k, R2 = 6.8 k, R3 = 10 k, R4 = 22 k and R5 = 33 k. To find the current through R4 flowing from node A to B, superposition may be used. Each source is again treated independently with the remaining sources replaced with their internal resistances. Calculate the current through R4 first considering E1 and then considering E2. Sum these results and record the three values in Table 10.5.2.

7. Assemble the circuit of Figure 10.3.2 using the values specified. Replace source E2 with a short and measure the current through R4. Be sure to note the direction of flow and record the result in Table 10.5.2.

8. Replace the short with source E2 and swap source E1 with a short. Measure the current through R4. Be sure to note the direction of flow and record the result in Table 10.5.2.

9. Remove the shorting wire and re-insert source E1. Both sources should now be in the circuit. Measure the current through R4 and record in Table 10.5.2. Be sure to note the direction. Determine and record the deviations between theory and experimental results.

10. Power is not a linear function as it is proportional to the square of either voltage or current. Consequently, superposition should not yield an accurate result when applied directly to power. Based on the measured currents in Table 10.5.2, calculate the power in R4 using E1-only and E2-only and record the values in Table 10.5.3. Adding these two powers yields the power as predicted by superposition. Determine this value and record it in Table 10.5.3. The true power in R4 may be determined from the total measured current flowing through it. Using the experimental current measured when both E1 and E2 were active (Table 10.5.2), determine the power in R4 and record it in Table 10.5.3.

## 10.4.3: Simulation

11. Build the circuit of Figure 10.3.2 in a simulator. Using the virtual DMM as an ammeter, determine the current through resistor R4 and compare it to the theoretical and measured values recorded in Table 10.5.2.

This page titled 4.1.4: Procedure is shared under a CC BY-NC-SA license and was authored, remixed, and/or curated by James M. Fiore.