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​ = 2 ΩR2​ = 8 Ω+−V1​6 VR3​6 Ω+−VR3​A+−V2​6 V

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

V1 = 6 VV2 = 6 VR1 = 2 ΩR2 = 8 ΩR3 = 6 Ω
VR3 = V
2.Easy
R1​ = 6 Ω+−V1​24 VR2​10 ΩAIs​2 A

Use superposition to find the node voltage VA (measured from ground).

V1 = 24 VIs = 2 AR1 = 6 ΩR2 = 10 Ω
VA = 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 = 2 V and Is = 6 mA, I = −4.1 mA; with Vs = 8 V and Is = 10 mA, I = −5.9 mA. Find the load current I when Vs = 5 V and Is = 10 mA.

2 V, 6 mA → −4.1 mA8 V, 10 mA → −5.9 mAVs = 5 V, Is = 10 mA
I = mA
4.Medium
R1​ = 15 ΩR3​ = 3 Ω+−V1​12 VR2​2 ΩAR4​8 Ω+−VR4​BIs​1.5 A

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

V1 = 12 VIs = 1.5 AR1 = 15 ΩR2 = 2 ΩR3 = 3 ΩR4 = 8 Ω
VR4 = V
5.Hard
R1​ = 30 ΩR2​ = 6 ΩIR2​R4​ = 2 Ω+−V1​9 VR3​15 ΩAIs​0.5 AB+−V2​9 V

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

V1 = 9 VIs = 0.5 AV2 = 9 VR1 = 30 ΩR2 = 6 ΩR3 = 15 ΩR4 = 2 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 = 12.5 mA. With V1 doubled and the other two unchanged, I = 11.5 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 = 12.5 mA2·V1: I = 11.5 mA−Is: I = −11.5 mA
I = mA

Answer key

  1. 1. VR3 = 4.737 V
  2. 2. VA = 7.5 V
  3. 3. I = −6.5 mA
  4. 4. VR4 = 5.364 V
  5. 5. IR2 = −0.3889 A
  6. 6. I = 11 mA

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