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

Use superposition to find the current I_R3 through R₃ in the direction of the arrow.

V₁ = 6 VV₂ = 18 VR₁ = 8 ΩR₂ = 2 ΩR₃ = 6 Ω

I_R3 = A

2.Easy

A linear resistive circuit contains two independent voltage sources, V₁ = 5 V and V₂ = 12 V. With both sources on, the current through the load resistor is I = −3.5 mA. With V₂ switched off (replaced by a short circuit) and V₁ unchanged, the load current is 16.5 mA. Find the load current I when V₁ is raised to 10 V and V₂ stays at 12 V.

I = −3.5 mA (both sources)I = 16.5 mA (only V₁)

I = mA

3.Medium

A linear resistive circuit contains one voltage source V_s and one current source I_s. The current I through a load resistor is measured twice: with V_s = 20 V and I_s = 4 mA, I = 9.6 mA; with V_s = 10 V and I_s = 1 mA, I = 4.9 mA. Find the load current I when V_s = 20 V and I_s = 2 mA.

20 V, 4 mA → 9.6 mA10 V, 1 mA → 4.9 mAV_s = 20 V, I_s = 2 mA

I = mA

4.Medium

Use superposition to find the voltage V_R4 across R₄ with the polarity shown.

V₁ = 30 VI_s = 4 AR₁ = 3 ΩR₂ = 4 ΩR₃ = 12 ΩR₄ = 8 Ω

V_R4 = V

5.Hard

Use superposition to find the current I_R2 through R₂ in the direction of the arrow.

V₁ = 15 VI_s = 1 AV₂ = 9 VR₁ = 2 ΩR₂ = 25 ΩR₃ = 6 ΩR₄ = 20 Ω

I_R2 = A

6.Hard

Use superposition to find the voltage V_R2 across R₂ with the polarity shown.

V₁ = 30 VI_s = 3 AV₂ = 30 VR₁ = 6 ΩR₂ = 5 ΩR₃ = 25 ΩR₄ = 3 Ω

V_R2 = V

Answer key

1. I_R3 = 2.053 A
2. I = 13 mA
3. I = 9.8 mA
4. V_R4 = −13.89 V
5. I_R2 = −0.4785 A
6. V_R2 = 17.6 V

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