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 ΩR2​ = 4 ΩIR2​+−V1​8 VR3​12 ΩA+−V2​12 V

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

V1 = 8 VV2 = 12 VR1 = 4 ΩR2 = 4 ΩR3 = 12 Ω
IR2 = A
2.Easy
R1​ = 5 ΩIR1​R2​ = 3 Ω+−V1​6 VR3​6 ΩA+−V2​24 V

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

V1 = 6 VV2 = 24 VR1 = 5 ΩR2 = 3 ΩR3 = 6 Ω
IR1 = A
3.Medium
R1​ = 4 ΩR3​ = 2 ΩIR3​+−V1​18 VR2​12 ΩAR4​2 ΩBIs​?

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

V1 = 18 VR1 = 4 ΩR2 = 12 ΩR3 = 2 ΩR4 = 2 Ω
Is = A
4.Medium
linear circuitVs​Is​IRL​

A linear resistive circuit contains one voltage source Vs and one current source Is. The current I through a load resistor is measured twice: with Vs = 4 V and Is = 2 mA, I = 6.8 mA; with Vs = 20 V and Is = 1 mA, I = 30.4 mA. Find the load current I when Vs = 6 V and Is = 2 mA.

4 V, 2 mA → 6.8 mA20 V, 1 mA → 30.4 mAVs = 6 V, Is = 2 mA
I = mA
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 = −8.5 mA. With V1 doubled and the other two unchanged, I = −1 mA. With the direction of Is reversed and the other two unchanged, I = 8.5 mA. Find the load current I when V2 is switched off and V1 and Is have their normal values.

normal: I = −8.5 mA2·V1: I = −1 mA−Is: I = 8.5 mA
I = mA
6.Hard
R1​ = 10 ΩR2​ = 25 ΩR4​ = 10 Ω+−V1​9 VR3​12 ΩIR3​AIs​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 = 9 VIs = 5 AR1 = 10 ΩR2 = 25 ΩR3 = 12 ΩR4 = 10 Ω
V2 = V

Answer key

  1. 1. IR2 = −0.8571 A
  2. 2. IR1 = −1.429 A
  3. 3. Is = 6.75 A
  4. 4. I = 9.8 mA
  5. 5. I = −1 mA
  6. 6. V2 = 18.5 V

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