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 ΩIR1​+−V1​20 VR2​4 ΩAIs​2 A

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

V1 = 20 VIs = 2 AR1 = 10 ΩR2 = 4 Ω
IR1 = A
2.Easy
R1​ = 12 ΩR2​ = 12 ΩIR2​+−V1​18 VR3​2 ΩA+−V2​24 V

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

V1 = 18 VV2 = 24 VR1 = 12 ΩR2 = 12 ΩR3 = 2 Ω
IR2 = A
3.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 = 6 V and Is = 2 mA, I = 13.5 mA; with Vs = 12 V and Is = 1 mA, I = 24.75 mA. Find the load current I when Vs = 12 V and Is = 2 mA.

6 V, 2 mA → 13.5 mA12 V, 1 mA → 24.75 mAVs = 12 V, Is = 2 mA
I = mA
4.Medium
R1​ = 3 ΩR3​ = 2 ΩIR3​+−V1​30 VR2​20 ΩAR4​8 ΩBIs​?

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

V1 = 30 VR1 = 3 ΩR2 = 20 ΩR3 = 2 ΩR4 = 8 Ω
Is = A
5.Hard
R1​ = 5 ΩR2​ = 25 ΩR4​ = 10 Ω+−V1​6 VR3​30 Ω+−VR3​AIs​2.5 AB+−V2​10 V

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

V1 = 6 VIs = 2.5 AV2 = 10 VR1 = 5 ΩR2 = 25 ΩR3 = 30 ΩR4 = 10 Ω
VR3 = V
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 = 17 mA. With V1 doubled and the other two unchanged, I = 23 mA. With the direction of Is reversed and the other two unchanged, I = 12 mA. Find the load current I when V2 is switched off and V1 and Is have their normal values.

normal: I = 17 mA2·V1: I = 23 mA−Is: I = 12 mA
I = mA

Answer key

  1. 1. IR1 = 2 A
  2. 2. IR2 = −1.563 A
  3. 3. I = 25.5 mA
  4. 4. Is = 3.261 A
  5. 5. VR3 = 8.4 V
  6. 6. I = 8.5 mA

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