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​ = 3 ΩR2​ = 6 Ω+−V1​20 VR3​2 ΩIR3​A+−V2​12 V

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

V1 = 20 VV2 = 12 VR1 = 3 ΩR2 = 6 ΩR3 = 2 Ω
IR3 = A
2.Easy
R1​ = 4 ΩR2​ = 5 ΩIR2​+−V1​24 VR3​4 ΩA+−V2​10 V

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

V1 = 24 VV2 = 10 VR1 = 4 ΩR2 = 5 ΩR3 = 4 Ω
IR2 = A
3.Medium
R1​ = 20 ΩR3​ = 8 ΩIR3​+−V1​10 VR2​10 ΩAR4​3 ΩBIs​?

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

V1 = 10 VR1 = 20 ΩR2 = 10 ΩR3 = 8 ΩR4 = 3 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 = 20 V and Is = 8 mA, I = 8.2 mA; with Vs = 20 V and Is = 10 mA, I = 9 mA. Find the load current I when Vs = 2 V and Is = 6 mA.

20 V, 8 mA → 8.2 mA20 V, 10 mA → 9 mAVs = 2 V, Is = 6 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 = 9 mA. With V1 doubled and the other two unchanged, I = 4.5 mA. With the direction of Is reversed and the other two unchanged, I = −1 mA. Find the load current I when V2 is switched off and V1 and Is have their normal values.

normal: I = 9 mA2·V1: I = 4.5 mA−Is: I = −1 mA
I = mA
6.Hard
R1​ = 8 ΩR2​ = 2 ΩR4​ = 15 Ω+−V1​9 VR3​25 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 = 9 VIs = 2.5 AR1 = 8 ΩR2 = 2 ΩR3 = 25 ΩR4 = 15 Ω
V2 = V

Answer key

  1. 1. IR3 = 4.333 A
  2. 2. IR2 = 0.2857 A
  3. 3. Is = 1.111 A
  4. 4. I = 2.9 mA
  5. 5. I = 0.5 mA
  6. 6. V2 = 18.37 V

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