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​ = 5 ΩR2​ = 5 Ω+−V1​20 VR3​3 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 = 5 ΩR2 = 5 ΩR3 = 3 Ω
IR3 = A
2.Easy
R1​ = 2 ΩR2​ = 3 Ω+−V1​18 VR3​5 ΩIR3​A+−V2​8 V

Use superposition to find the contribution IR3′ of V1 alone to the current IR3 through R3 in the direction of the arrow.

V1 = 18 VV2 = 8 VR1 = 2 ΩR2 = 3 ΩR3 = 5 Ω
IR3′ = A
3.Medium
R1​ = 20 ΩIR1​R3​ = 4 Ω+−V1​18 VR2​20 ΩAR4​12 ΩBIs​1.5 A

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

V1 = 18 VIs = 1.5 AR1 = 20 ΩR2 = 20 ΩR3 = 4 ΩR4 = 12 Ω
IR1 = A
4.Medium
R1​ = 15 ΩR3​ = 15 Ω+−V1​15 VR2​4 Ω+−VR2​AR4​15 ΩBIs​3 A

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

V1 = 15 VIs = 3 AR1 = 15 ΩR2 = 4 ΩR3 = 15 ΩR4 = 15 Ω
VR2 = V
5.Hard
R1​ = 4 ΩR2​ = 2 ΩR4​ = 5 Ω+−V1​30 VR3​2 ΩIR3​AIs​6 AB+−V2​9 V

Use superposition to find the power PR3 absorbed by R3.

V1 = 30 VIs = 6 AV2 = 9 VR1 = 4 ΩR2 = 2 ΩR3 = 2 ΩR4 = 5 Ω
PR3 = 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 = 17 mA. With V1 doubled and the other two unchanged, I = 20.5 mA. With the direction of Is reversed and the other two unchanged, I = 13 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 = 20.5 mA−Is: I = 13 mA
I = mA

Answer key

  1. 1. IR3 = 3.636 A
  2. 2. IR3′ = 1.742 A
  3. 3. IR1 = 0.2769 A
  4. 4. VR2 = 7.143 V
  5. 5. PR3 = 107.2 W
  6. 6. I = 5.5 mA

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