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​R2​ = 5 Ω+−V1​12 VR3​12 ΩA+−V2​6 V

Use superposition to find the contribution IR1″ of V2 alone to the current IR1 through R1 in the direction of the arrow.

V1 = 12 VV2 = 6 VR1 = 4 ΩR2 = 5 ΩR3 = 12 Ω
IR1″ = A
2.Easy
R1​ = 12 ΩIR1​R2​ = 5 Ω+−V1​24 VR3​4 ΩA+−V2​24 V

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

V1 = 24 VV2 = 24 VR1 = 12 ΩR2 = 5 ΩR3 = 4 Ω
IR1 = A
3.Medium
R1​ = 15 ΩR3​ = 20 Ω+−V1​30 VR2​2 ΩAR4​20 Ω−+VR4​BIs​2 A

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

V1 = 30 VIs = 2 AR1 = 15 ΩR2 = 2 ΩR3 = 20 ΩR4 = 20 Ω
VR4 = V
4.Medium
R1​ = 5 ΩR3​ = 15 ΩIR3​+−V1​9 VR2​3 ΩAR4​5 ΩBIs​2 A

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

V1 = 9 VIs = 2 AR1 = 5 ΩR2 = 3 ΩR3 = 15 ΩR4 = 5 Ω
IR3 = 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 = 10.5 mA. With V1 doubled and the other two unchanged, I = 9 mA. With the direction of Is reversed and the other two unchanged, I = −1.5 mA. Find the load current I when V2 is switched off and V1 and Is have their normal values.

normal: I = 10.5 mA2·V1: I = 9 mA−Is: I = −1.5 mA
I = mA
6.Hard
R1​ = 20 ΩR2​ = 8 ΩR4​ = 20 ΩIR4​+−V1​10 VR3​4 ΩAIs​2.5 AB+−V2​5 V

Use superposition to find the current IR4 through R4 in the direction of the arrow.

V1 = 10 VIs = 2.5 AV2 = 5 VR1 = 20 ΩR2 = 8 ΩR3 = 4 ΩR4 = 20 Ω
IR4 = A

Answer key

  1. 1. IR1″ = −0.5625 A
  2. 2. IR1 = 0.9375 A
  3. 3. VR4 = −22.54 V
  4. 4. IR3 = −0.3029 A
  5. 5. I = 4.5 mA
  6. 6. IR4 = 0.7979 A

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