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​18 VR2​3 ΩAIs​3 A

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

V1 = 18 VIs = 3 AR1 = 4 ΩR2 = 3 Ω
IR1 = A
2.Easy
R1​ = 5 Ω+−V1​8 VR2​10 ΩIR2​AIs​3 A

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

V1 = 8 VIs = 3 AR1 = 5 ΩR2 = 10 Ω
IR2 = A
3.Medium
R1​ = 8 ΩR3​ = 3 Ω+−V1​30 VR2​10 ΩAR4​15 Ω+−VR4​BIs​2.5 A

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

V1 = 30 VIs = 2.5 AR1 = 8 ΩR2 = 10 ΩR3 = 3 ΩR4 = 15 Ω
VR4 = V
4.Medium
R1​ = 12 ΩR3​ = 6 ΩIR3​+−V1​24 VR2​5 ΩAR4​6 ΩBIs​1.5 A

Use superposition to find the power PR3 absorbed by R3.

V1 = 24 VIs = 1.5 AR1 = 12 ΩR2 = 5 ΩR3 = 6 ΩR4 = 6 Ω
PR3 = W
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 = 3.5 mA. With V1 doubled and the other two unchanged, I = −7.5 mA. With the direction of Is reversed and the other two unchanged, I = −2.5 mA. Find the load current I when V2 is switched off and V1 and Is have their normal values.

normal: I = 3.5 mA2·V1: I = −7.5 mA−Is: I = −2.5 mA
I = mA
6.Hard
R1​ = 20 ΩR2​ = 5 Ω−+VR2​R4​ = 3 Ω+−V1​12 VR3​15 ΩAIs​4 AB−+V2​12 V

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

V1 = 12 VIs = 4 AV2 = 12 VR1 = 20 ΩR2 = 5 ΩR3 = 15 ΩR4 = 3 Ω
VR2 = V

Answer key

  1. 1. IR1 = 1.286 A
  2. 2. IR2 = −0.4667 A
  3. 3. VR4 = 23.58 V
  4. 4. PR3 = 0.09375 W
  5. 5. I = −8 mA
  6. 6. VR2 = −1.552 V

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