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​ = 3 ΩIR2​+−V1​6 VR3​12 ΩA+−V2​8 V

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

V1 = 6 VV2 = 8 VR1 = 10 ΩR2 = 3 ΩR3 = 12 Ω
IR2 = A
2.Easy
R1​ = 5 ΩR2​ = 2 Ω+−V1​6 VR3​6 ΩIR3​A+−V2​18 V

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

V1 = 6 VV2 = 18 VR1 = 5 ΩR2 = 2 ΩR3 = 6 Ω
IR3 = A
3.Medium
R1​ = 15 ΩR3​ = 5 Ω+−V1​6 VR2​10 Ω+−VR2​AR4​3 ΩBIs​5 A

Use superposition to find the voltage VR2 across R2 with the polarity shown.

V1 = 6 VIs = 5 AR1 = 15 ΩR2 = 10 ΩR3 = 5 ΩR4 = 3 Ω
VR2 = V
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 = 10 mA, I = 10 mA; with Vs = 20 V and Is = 10 mA, I = 42 mA. Find the load current I when Vs = 5 V and Is = 3 mA.

4 V, 10 mA → 10 mA20 V, 10 mA → 42 mAVs = 5 V, Is = 3 mA
I = mA
5.Hard
R1​ = 12 ΩR2​ = 4 ΩR4​ = 8 Ω+−V1​24 VR3​15 ΩIR3​AIs​4 AB+−V2​?

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

V1 = 24 VIs = 4 AR1 = 12 ΩR2 = 4 ΩR3 = 15 ΩR4 = 8 Ω
V2 = 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 = 33 mA. With V1 doubled and the other two unchanged, I = 43.5 mA. With the direction of Is reversed and the other two unchanged, I = 9 mA. Find the load current I when V2 is switched off and V1 and Is have their normal values.

normal: I = 33 mA2·V1: I = 43.5 mA−Is: I = 9 mA
I = mA

Answer key

  1. 1. IR2 = −0.5591 A
  2. 2. IR3 = 1.962 A
  3. 3. VR2 = −5.057 V
  4. 4. I = 10.6 mA
  5. 5. V2 = 8 V
  6. 6. I = 22.5 mA

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