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​ = 4 ΩIR1​+−V1​24 VR2​8 ΩAIs​1 A

Use superposition to find the current IR1 through R1 in the direction of the arrow.

V1 = 24 VIs = 1 AR1 = 4 ΩR2 = 8 Ω
IR1 = A
2.Easy
R1​ = 4 ΩR2​ = 3 Ω+−V1​10 VR3​2 Ω+−VR3​A+−V2​10 V

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

V1 = 10 VV2 = 10 VR1 = 4 ΩR2 = 3 ΩR3 = 2 Ω
VR3 = V
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 = 4 V and Is = 6 mA, I = 6.4 mA; with Vs = 6 V and Is = 6 mA, I = 8.4 mA. Find the load current I when Vs = 5 V and Is = 8 mA.

4 V, 6 mA → 6.4 mA6 V, 6 mA → 8.4 mAVs = 5 V, Is = 8 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 = 15 V and Is = 4 mA, I = 29 mA; with Vs = 20 V and Is = 2 mA, I = 39.5 mA. Find the load current I when Vs = 20 V and Is = 8 mA.

15 V, 4 mA → 29 mA20 V, 2 mA → 39.5 mAVs = 20 V, Is = 8 mA
I = mA
5.Hard
R1​ = 30 ΩR2​ = 12 ΩIR2​R4​ = 10 Ω+−V1​10 VR3​12 ΩAIs​2 AB−+V2​12 V

Use superposition to find the power PR2 absorbed by R2.

V1 = 10 VIs = 2 AV2 = 12 VR1 = 30 ΩR2 = 12 ΩR3 = 12 ΩR4 = 10 Ω
PR2 = W
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 = 9.5 mA. With V1 doubled and the other two unchanged, I = 17 mA. With the direction of Is reversed and the other two unchanged, I = 11.5 mA. Find the load current I when V2 is switched off and V1 and Is have their normal values.

normal: I = 9.5 mA2·V1: I = 17 mA−Is: I = 11.5 mA
I = mA

Answer key

  1. 1. IR1 = 1.333 A
  2. 2. VR3 = 5.385 V
  3. 3. I = 8.2 mA
  4. 4. I = 38 mA
  5. 5. PR2 = 15.6 W
  6. 6. I = 6.5 mA

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