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​ = 8 ΩIR1​R2​ = 4 Ω+−V1​10 VR3​3 ΩA+−V2​18 V

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

V1 = 10 VV2 = 18 VR1 = 8 ΩR2 = 4 ΩR3 = 3 Ω
IR1″ = A
2.Easy
R1​ = 5 ΩIR1​R2​ = 6 Ω+−V1​15 VR3​12 ΩA+−V2​24 V

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

V1 = 15 VV2 = 24 VR1 = 5 ΩR2 = 6 ΩR3 = 12 Ω
IR1 = A
3.Medium
R1​ = 4 ΩR3​ = 4 Ω+−V1​30 VR2​6 ΩIR2​AR4​6 ΩBIs​5 A

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

V1 = 30 VIs = 5 AR1 = 4 ΩR2 = 6 ΩR3 = 4 ΩR4 = 6 Ω
IR2 = A
4.Medium
R1​ = 20 ΩR3​ = 5 Ω+−V1​9 VR2​6 ΩAR4​10 Ω+−VR4​BIs​1 A

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

V1 = 9 VIs = 1 AR1 = 20 ΩR2 = 6 ΩR3 = 5 ΩR4 = 10 Ω
VR4 = V
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 mA. With V1 doubled and the other two unchanged, I = 3.5 mA. With the direction of Is reversed and the other two unchanged, I = −18 mA. Find the load current I when V2 is switched off and V1 and Is have their normal values.

normal: I = 3 mA2·V1: I = 3.5 mA−Is: I = −18 mA
I = mA
6.Hard
R1​ = 8 ΩR2​ = 2 ΩR4​ = 3 ΩIR4​+−V1​18 VR3​15 ΩAIs​3 AB−+V2​10 V

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

V1 = 18 VIs = 3 AV2 = 10 VR1 = 8 ΩR2 = 2 ΩR3 = 15 ΩR4 = 3 Ω
IR4 = A

Answer key

  1. 1. IR1″ = −0.7941 A
  2. 2. IR1 = −0.1111 A
  3. 3. IR2 = 3.387 A
  4. 4. VR4 = −3.843 V
  5. 5. I = 11 mA
  6. 6. IR4 = −4.247 A

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