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
R1​ = 12 ΩR2​ = 12 Ω+−V1​24 VR3​12 Ω+−VR3​A+−V2​6 V

Use superposition to find the voltage VR3 across R3 with the polarity shown.

V1 = 24 VV2 = 6 VR1 = 12 ΩR2 = 12 ΩR3 = 12 Ω
VR3 = V
2.Easy
R1​ = 4 ΩR2​ = 5 Ω+−V1​20 VR3​12 ΩIR3​A+−V2​20 V

Use superposition to find the current IR3 through R3 in the direction of the arrow.

V1 = 20 VV2 = 20 VR1 = 4 ΩR2 = 5 ΩR3 = 12 Ω
IR3 = 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 = 15 V and Is = 5 mA, I = 33.75 mA; with Vs = 10 V and Is = 2 mA, I = 21.5 mA. Find the load current I when Vs = 12 V and Is = 3 mA.

15 V, 5 mA → 33.75 mA10 V, 2 mA → 21.5 mAVs = 12 V, Is = 3 mA
I = mA
4.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 = 6 V and Is = 6 mA, I = 0.6 mA; with Vs = 5 V and Is = 2 mA, I = 1.4 mA. Find the load current I when Vs = 2 V and Is = 6 mA.

6 V, 6 mA → 0.6 mA5 V, 2 mA → 1.4 mAVs = 2 V, Is = 6 mA
I = mA
5.Hard
R1​ = 4 ΩR2​ = 30 ΩIR2​R4​ = 20 Ω+−V1​36 VR3​2 ΩAIs​6 AB+−V2​10 V

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

V1 = 36 VIs = 6 AV2 = 10 VR1 = 4 ΩR2 = 30 ΩR3 = 2 ΩR4 = 20 Ω
IR2 = A
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 = 4.5 mA. With V1 doubled and the other two unchanged, I = 7.5 mA. With the direction of Is reversed and the other two unchanged, I = 15.5 mA. Find the load current I when V2 is switched off and V1 and Is have their normal values.

normal: I = 4.5 mA2·V1: I = 7.5 mA−Is: I = 15.5 mA
I = mA

Answer key

  1. 1. VR3 = 10 V
  2. 2. IR3 = 1.406 A
  3. 3. I = 26.25 mA
  4. 4. I = −1 mA
  5. 5. IR2 = −2.377 A
  6. 6. I = −2.5 mA

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