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​ = 2 ΩIR1​R2​ = 8 Ω+−V1​10 VR3​10 ΩA+−V2​12 V

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

V1 = 10 VV2 = 12 VR1 = 2 ΩR2 = 8 ΩR3 = 10 Ω
IR1 = A
2.Easy
linear circuitV1​ = 20 VV2​ = 15 VIRL​

A linear resistive circuit contains two independent voltage sources, V1 = 20 V and V2 = 15 V. With both sources on, the current through the load resistor is I = 24.5 mA. With V2 switched off (replaced by a short circuit) and V1 unchanged, the load current is 8 mA. Find the load current I when V1 is switched off and only V2 = 15 V is active.

I = 24.5 mA (both sources)I = 8 mA (only V1)
I = mA
3.Medium
R1​ = 5 ΩR3​ = 8 ΩIR3​+−V1​12 VR2​4 ΩAR4​15 ΩBIs​?

Find the value of the current source Is (direction as shown) that makes the current IR3 through R3 equal to zero.

V1 = 12 VR1 = 5 ΩR2 = 4 ΩR3 = 8 ΩR4 = 15 Ω
Is = A
4.Medium
R1​ = 3 ΩR3​ = 2 Ω+−V1​24 VR2​5 ΩAR4​20 Ω−+VR4​BIs​3 A

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

V1 = 24 VIs = 3 AR1 = 3 ΩR2 = 5 ΩR3 = 2 ΩR4 = 20 Ω
VR4 = V
5.Hard
R1​ = 12 ΩR2​ = 15 ΩR4​ = 8 ΩIR4​+−V1​9 VR3​12 ΩAIs​5 AB−+V2​12 V

Use superposition to find the power PR4 absorbed by R4.

V1 = 9 VIs = 5 AV2 = 12 VR1 = 12 ΩR2 = 15 ΩR3 = 12 ΩR4 = 8 Ω
PR4 = W
6.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 = −1.5 mA. With V1 doubled and the other two unchanged, I = 1.5 mA. With the direction of Is reversed and the other two unchanged, I = −10.5 mA. Find the load current I when V2 is switched off and V1 and Is have their normal values.

normal: I = −1.5 mA2·V1: I = 1.5 mA−Is: I = −10.5 mA
I = mA

Answer key

  1. 1. IR1 = 0.5172 A
  2. 2. I = 16.5 mA
  3. 3. Is = 0.3556 A
  4. 4. VR4 = −2.827 V
  5. 5. PR4 = 140.4 W
  6. 6. I = 7.5 mA

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