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​ = 10 ΩR2​ = 5 Ω+−V1​12 VR3​12 Ω+−VR3​A+−V2​10 V

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

V1 = 12 VV2 = 10 VR1 = 10 ΩR2 = 5 ΩR3 = 12 Ω
VR3 = V
2.Easy
R1​ = 10 ΩR2​ = 5 ΩIR2​+−V1​6 VR3​6 ΩA+−V2​20 V

Use superposition to find the contribution IR2″ of V2 alone to the current IR2 through R2 in the direction of the arrow.

V1 = 6 VV2 = 20 VR1 = 10 ΩR2 = 5 ΩR3 = 6 Ω
IR2″ = A
3.Medium
R1​ = 10 ΩR3​ = 6 Ω+−V1​12 VR2​8 ΩAR4​2 Ω+−VR4​BIs​1.5 A

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

V1 = 12 VIs = 1.5 AR1 = 10 ΩR2 = 8 ΩR3 = 6 ΩR4 = 2 Ω
VR4 = V
4.Medium
R1​ = 8 ΩR3​ = 12 ΩIR3​+−V1​24 VR2​15 ΩAR4​15 ΩBIs​2 A

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

V1 = 24 VIs = 2 AR1 = 8 ΩR2 = 15 ΩR3 = 12 ΩR4 = 15 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 = 21.5 mA. With V1 doubled and the other two unchanged, I = 33.5 mA. With the direction of Is reversed and the other two unchanged, I = 25.5 mA. Find the load current I when V2 is switched off and V1 and Is have their normal values.

normal: I = 21.5 mA2·V1: I = 33.5 mA−Is: I = 25.5 mA
I = mA
6.Hard
R1​ = 8 ΩR2​ = 3 ΩR4​ = 30 Ω+−V1​10 VR3​3 ΩIR3​AIs​2.5 AB+−V2​?

Find the value of the voltage source V2 (polarity as shown) that makes the current IR3 through R3 equal to zero.

V1 = 10 VIs = 2.5 AR1 = 8 ΩR2 = 3 ΩR3 = 3 ΩR4 = 30 Ω
V2 = V

Answer key

  1. 1. VR3 = 8.348 V
  2. 2. IR2″ = −2.286 A
  3. 3. VR4 = −1.661 V
  4. 4. IR3 = −0.4453 A
  5. 5. I = 10 mA
  6. 6. V2 = 33.75 V

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