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​ = 8 ΩR2​ = 10 Ω+−V1​20 VR3​3 Ω+−VR3​A+−V2​10 V

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

V1 = 20 VV2 = 10 VR1 = 8 ΩR2 = 10 ΩR3 = 3 Ω
VR3 = V
2.Easy
linear circuitV1​ = 12 VV2​ = 24 VIRL​

A linear resistive circuit contains two independent voltage sources, V1 = 12 V and V2 = 24 V. With both sources on, the current through the load resistor is I = −2.5 mA. With V2 switched off (replaced by a short circuit) and V1 unchanged, the load current is 12 mA. Find the load current I when V1 is raised to 24 V and V2 stays at 24 V.

I = −2.5 mA (both sources)I = 12 mA (only V1)
I = mA
3.Medium
R1​ = 6 ΩIR1​R3​ = 6 Ω+−V1​12 VR2​12 ΩAR4​3 ΩBIs​3 A

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

V1 = 12 VIs = 3 AR1 = 6 ΩR2 = 12 ΩR3 = 6 ΩR4 = 3 Ω
IR1 = 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 = 8 V and Is = 4 mA, I = 8.4 mA; with Vs = 10 V and Is = 3 mA, I = 11.1 mA. Find the load current I when Vs = 4 V and Is = 4 mA.

8 V, 4 mA → 8.4 mA10 V, 3 mA → 11.1 mAVs = 4 V, Is = 4 mA
I = mA
5.Hard
R1​ = 15 ΩR2​ = 10 ΩR4​ = 5 Ω+−V1​15 VR3​25 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 = 15 VIs = 4 AR1 = 15 ΩR2 = 10 ΩR3 = 25 ΩR4 = 5 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 = −27.5 mA. With V1 doubled and the other two unchanged, I = −35.5 mA. With the direction of Is reversed and the other two unchanged, I = −4.5 mA. Find the load current I when V2 is switched off and V1 and Is have their normal values.

normal: I = −27.5 mA2·V1: I = −35.5 mA−Is: I = −4.5 mA
I = mA

Answer key

  1. 1. VR3 = 6.269 V
  2. 2. I = 9.5 mA
  3. 3. IR1 = 1.538 A
  4. 4. I = 3.6 mA
  5. 5. V2 = 5 V
  6. 6. I = −19.5 mA

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