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 ΩR2​ = 12 Ω+−V1​10 VR3​8 Ω+−VR3​A+−V2​18 V

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

V1 = 10 VV2 = 18 VR1 = 2 ΩR2 = 12 ΩR3 = 8 Ω
VR3 = V
2.Easy
R1​ = 10 Ω+−V1​20 VR2​3 ΩIR2​AIs​1 A

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

V1 = 20 VIs = 1 AR1 = 10 ΩR2 = 3 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 = 8 V and Is = 3 mA, I = 2.5 mA; with Vs = 8 V and Is = 1 mA, I = 1.9 mA. Find the load current I when Vs = 10 V and Is = 6 mA.

8 V, 3 mA → 2.5 mA8 V, 1 mA → 1.9 mAVs = 10 V, Is = 6 mA
I = mA
4.Medium
R1​ = 10 ΩR3​ = 3 ΩIR3​+−V1​30 VR2​8 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 = 10 ΩR2 = 8 ΩR3 = 3 ΩR4 = 8 Ω
Is = A
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 = −3 mA. With V1 doubled and the other two unchanged, I = −7.5 mA. With the direction of Is reversed and the other two unchanged, I = −22 mA. Find the load current I when V2 is switched off and V1 and Is have their normal values.

normal: I = −3 mA2·V1: I = −7.5 mA−Is: I = −22 mA
I = mA
6.Hard
R1​ = 10 ΩR2​ = 6 ΩR4​ = 6 Ω+−V1​15 VR3​6 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 = 15 VIs = 5 AR1 = 10 ΩR2 = 6 ΩR3 = 6 ΩR4 = 6 Ω
V2 = V

Answer key

  1. 1. VR3 = 9.176 V
  2. 2. IR2 = 2.308 A
  3. 3. I = 3.8 mA
  4. 4. Is = 1.667 A
  5. 5. I = 5 mA
  6. 6. V2 = 12 V

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