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​18 VR3​10 ΩIR3​A+−V2​10 V

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

V1 = 18 VV2 = 10 VR1 = 12 ΩR2 = 12 ΩR3 = 10 Ω
IR3 = A
2.Easy
R1​ = 12 ΩIR1​R2​ = 3 Ω+−V1​12 VR3​12 ΩA+−V2​24 V

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

V1 = 12 VV2 = 24 VR1 = 12 ΩR2 = 3 ΩR3 = 12 Ω
IR1 = 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 = 6 V and Is = 10 mA, I = 4.9 mA; with Vs = 20 V and Is = 10 mA, I = 10.5 mA. Find the load current I when Vs = 5 V and Is = 1 mA.

6 V, 10 mA → 4.9 mA20 V, 10 mA → 10.5 mAVs = 5 V, Is = 1 mA
I = mA
4.Medium
R1​ = 2 ΩR3​ = 6 Ω+−V1​24 VR2​15 ΩAR4​5 Ω+−VR4​BIs​1 A

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

V1 = 24 VIs = 1 AR1 = 2 ΩR2 = 15 ΩR3 = 6 ΩR4 = 5 Ω
VR4 = V
5.Hard
R1​ = 4 ΩR2​ = 2 Ω+−VR2​R4​ = 10 Ω+−V1​6 VR3​15 ΩAIs​0.5 AB+−V2​12 V

Use superposition to find the voltage VR2 across R2 with the polarity shown.

V1 = 6 VIs = 0.5 AV2 = 12 VR1 = 4 ΩR2 = 2 ΩR3 = 15 ΩR4 = 10 Ω
VR2 = V
6.Hard
R1​ = 15 ΩR2​ = 10 ΩR4​ = 15 Ω+−V1​15 VR3​8 ΩIR3​AIs​2.5 AB+−V2​?

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

V1 = 15 VIs = 2.5 AR1 = 15 ΩR2 = 10 ΩR3 = 8 ΩR4 = 15 Ω
V2 = V

Answer key

  1. 1. IR3 = 0.875 A
  2. 2. IR1 = −0.5 A
  3. 3. I = 2.25 mA
  4. 4. VR4 = 11.34 V
  5. 5. VR2 = −1.618 V
  6. 6. V2 = 12.5 V

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