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 ΩR2​ = 12 Ω+−V1​24 VR3​5 Ω+−VR3​A+−V2​6 V

Use superposition to find the contribution VR3′ of V1 alone to the voltage VR3 across R3 with the polarity shown.

V1 = 24 VV2 = 6 VR1 = 4 ΩR2 = 12 ΩR3 = 5 Ω
VR3′ = V
2.Easy
R1​ = 12 ΩR2​ = 6 ΩIR2​+−V1​12 VR3​8 ΩA+−V2​24 V

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

V1 = 12 VV2 = 24 VR1 = 12 ΩR2 = 6 ΩR3 = 8 Ω
IR2 = A
3.Medium
R1​ = 3 ΩR3​ = 2 Ω+−V1​15 VR2​2 ΩAR4​2 ΩIR4​BIs​2.5 A

Use superposition to find the power PR4 absorbed by R4.

V1 = 15 VIs = 2.5 AR1 = 3 ΩR2 = 2 ΩR3 = 2 ΩR4 = 2 Ω
PR4 = W
4.Medium
R1​ = 20 ΩIR1​R3​ = 15 Ω+−V1​30 VR2​20 ΩAR4​20 ΩBIs​2.5 A

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

V1 = 30 VIs = 2.5 AR1 = 20 ΩR2 = 20 ΩR3 = 15 ΩR4 = 20 Ω
IR1 = A
5.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 mA. With V1 doubled and the other two unchanged, I = 4.5 mA. With the direction of Is reversed and the other two unchanged, I = 2 mA. Find the load current I when V2 is switched off and V1 and Is have their normal values.

normal: I = 9 mA2·V1: I = 4.5 mA−Is: I = 2 mA
I = mA
6.Hard
R1​ = 25 ΩR2​ = 25 ΩR4​ = 10 Ω+−V1​5 VR3​15 Ω+−VR3​AIs​5 AB+−V2​18 V

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

V1 = 5 VIs = 5 AV2 = 18 VR1 = 25 ΩR2 = 25 ΩR3 = 15 ΩR4 = 10 Ω
VR3 = V

Answer key

  1. 1. VR3′ = 11.25 V
  2. 2. IR2 = −1.778 A
  3. 3. PR4 = 14.5 W
  4. 4. IR1 = 0.3611 A
  5. 5. I = −1 mA
  6. 6. VR3 = −5.282 V

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