Superposition worksheet with answers

Free printable Superposition worksheet: 6 problems from easy to exam level, with an answer key. Print it or save it as a PDF.

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1.Easy
linear circuitV1​ = 9 VV2​ = 9 VIRL​

A linear resistive circuit contains two independent voltage sources, V1 = 9 V and V2 = 9 V. With both sources on, the current through the load resistor is I = 30 mA. With V2 switched off (replaced by a short circuit) and V1 unchanged, the load current is 13 mA. Find the load current I when V1 is switched off and only V2 = 9 V is active.

I = 30 mA (both sources)I = 13 mA (only V1)
I = mA
2.Easy
R1​ = 2 ΩR2​ = 8 ΩIR2​+−V1​18 VR3​5 ΩA+−V2​8 V

Use superposition to find the current IR2 through R2 in the direction of the arrow.

V1 = 18 VV2 = 8 VR1 = 2 ΩR2 = 8 ΩR3 = 5 Ω
IR2 = A
3.Medium
linear circuitVs​Is​IRL​

A linear resistive circuit contains one voltage source Vs and one current source Is. The current I through a load resistor is measured twice: with Vs = 5 V and Is = 8 mA, I = 5.2 mA; with Vs = 5 V and Is = 2 mA, I = 2.8 mA. Find the load current I when Vs = 8 V and Is = 4 mA.

5 V, 8 mA → 5.2 mA5 V, 2 mA → 2.8 mAVs = 8 V, Is = 4 mA
I = mA
4.Medium
R1​ = 10 ΩR3​ = 8 Ω+−V1​12 VR2​4 ΩAR4​10 Ω+−VR4​BIs​3 A

Use superposition to find the voltage VR4 across R4 with the polarity shown.

V1 = 12 VIs = 3 AR1 = 10 ΩR2 = 4 ΩR3 = 8 ΩR4 = 10 Ω
VR4 = V
5.Hard
R1​ = 20 ΩR2​ = 15 ΩR4​ = 8 Ω+−V1​9 VR3​15 ΩIR3​AIs​5 AB+−V2​?

Find the value of the voltage source V2 (polarity as shown) that makes the current IR3 through R3 equal to zero.

V1 = 9 VIs = 5 AR1 = 20 ΩR2 = 15 ΩR3 = 15 ΩR4 = 8 Ω
V2 = V
6.Hard
linear circuitV1​V2​Is​IRL​

A linear resistive circuit contains three independent sources: V1, V2 and Is. The current I through a load is measured three times. With all sources at their normal values, I = 17 mA. With V1 doubled and the other two unchanged, I = 19 mA. With the direction of Is reversed and the other two unchanged, I = −3 mA. Find the load current I when V2 is switched off and V1 and Is have their normal values.

normal: I = 17 mA2·V1: I = 19 mA−Is: I = −3 mA
I = mA

Answer key

  1. 1. I = 17 mA
  2. 2. IR2 = 0.5152 A
  3. 3. I = 4.8 mA
  4. 4. VR4 = 17.26 V
  5. 5. V2 = 29.65 V
  6. 6. I = 12 mA

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