The Superposition Theorem Objectives 1. Apply the superposition to linear circuits with more than one voltage source. 2. Construct a circuit with two voltage sources, solve for currents and voltages throughout and verify your computation by measurements. Resistors Needed: One each: 4.7 ks2, 6.8 ks2, 10 ks Procedure 1. Obtain the resistors listed in Table 1. Measure each resistor and record the value in Table 1. 2. Construct the circuit shown in Figure 1. This circuit has two voltage sources connected to a common reference ground. R1 R2 C VS1= +5V 4.7K Q 6.8KQ VS2= +10V R3 10.0K Q B Common Ground D Figure 1 3. Remove the 10 V source and place a jumper (wire) between the points labeled C and D, as shown in Figure 2. This jumper represents the internal resistance of the 10 V power supply. VS1= +5V A R1 R2 C w 4.7K Q 6.8K Q R3 10.0K Jumper B D Figure 2 5. 4. Compute the total resistance RT, seen by the 5v source. Then temporarily remove the 5v source and measure the resistance between points A and B to confirm your calculation. Record the computed and measured values in Table 2. Use the source voltage, Vsi, and the total resistance to compute the total current, Ir, from the 5v source. This current is through Ri, so record it as I₁ in Table 3. Use the current divider rule to determine the currents in R2 and R3. Attach all calculations to lab report. Record all three currents as positive values in Table 3. This will be the assigned reference for the direction of current. Mark the magnitude and direction of the current in Figure 2. 6. Use the currents computed in step 5 and the measured resistances to calculate the expected voltage across each resistor of Figure 2. Then connect the 5v power supply and measure the actual voltages present in this circuit. Record the computed and measured voltages in Table 3. Since all currents in step 5 were considered positive, all voltages in this step are also positive. 7. Remove the 5v source from the circuit and move the jumper from between points C and othe between points A and B. Compute the total resistance between points C and D. Measure the resistance to confirm your calculation. Record the computed and measured resistance in Table 2. 8. Compute the current through each resistor in Figure 3. Note that this time the total current is through R2 and divides between Ri and Rs. Mark the magnitude and direction of the current on Figure 3. Important: Record the current as a positive current if it is in the same direction as recorded in step 5 and as a negative current if it is in the opposite direction as in step 4. Record the computed currents in Table 3. R1 R2 C w 4.7K Q 6.8K Q VS2= +10V JUMPER R3 10.0K B D Figure 3 9. Use the currents computed in step 8 and the measured resistances to compute the voltage drops across each resistor. Record the computed voltage drops in Table 3. If the current through a resistor was a positive current, record the resistor's voltage as a positive voltage. If a current was a negative current, record the voltage as a negative voltage. Then connect the 10v source as illustrated in Figure 3, measure, and record the voltages. The measured voltages should confirm your calculation. 10. Compute the algebraic sum of the currents and voltage listed in Table 3. Enter the computed sums in Table 3. Then replace the jumper between A and B with the 5v source, as shown in the original circuit in Figure 1. Measure the voltage across each resistor in this circuit. The measured voltages should agree with the algebraic sums. Record the measured results in Table 3. Data Attach work showing all calculations to lab Table 1 Listed Measured Value Value R₁ 4.7 ΚΩ R2 6.8 ΚΩ Ra 10.0 ΚΩ Quantity Computed Measured Step 4 Rr (Vsi operating alone) Table 2 Computed and measured resistances. Step 7 Rr (Vs2 operating alone) Table 3 Computed and measured current and voltage. Computed Current 1 Computed Voltage 12 h Step 5 V₁ V₂ V3 V₁ Measured Voltage V₂ V3 Step 6 Step 8 Step 9 Step 10 (totals) Conclusion Evaluation and Review Questions 1. (a) Prove the Kirchhoff's voltage law is valid for the circuit in Figure 1. Do this by substituting the measured algebraic sums from Table 3 into a loop equation written around the outside loop of the circuit. (b) Prove Kirchhoff's current law is valid for the circuit of Figure I by writing an equation showing the currents entering a junction are equal to the currents leaving the junction. 2. Use the signed currents computed in step 10. If an algebraic sum in Table 3 is negative, what does this indicate? 3. What would be the effect on the final result if you had been directed to record all currents in step 5 as negative currents instead of positive currents? 4. In your own words, list the steps required to apply the superposition theorem. 5. Use the superposition theorem to find the current in R2 in Figure 4. Show all work. R₁ 10012 ww VSI 20v Vst 40v Figure 4 R₂ 2000 www R₁ 30052