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

A linear resistive circuit contains two independent voltage sources, V₁ = 20 V and V₂ = 12 V. With both sources on, the current through the load resistor is I = 14.5 mA. With V₂ switched off (replaced by a short circuit) and V₁ unchanged, the load current is −5.5 mA. Find the load current I when V₁ is switched off and only V₂ = 12 V is active.

I = 14.5 mA (both sources)I = −5.5 mA (only V₁)

I = mA

2.Easy

Use superposition to find the contribution I_R1′ of V₁ alone to the current I_R1 through R₁ in the direction of the arrow.

V₁ = 12 VV₂ = 20 VR₁ = 4 ΩR₂ = 12 ΩR₃ = 3 Ω

I_R1′ = A

3.Medium

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

V₁ = 10 VI_s = 2 AR₁ = 20 ΩR₂ = 2 ΩR₃ = 20 ΩR₄ = 10 Ω

I_R2 = A

4.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 = 12 V and I_s = 2 mA, I = 7.4 mA; with V_s = 8 V and I_s = 5 mA, I = 5.3 mA. Find the load current I when V_s = 12 V and I_s = 3 mA.

12 V, 2 mA → 7.4 mA8 V, 5 mA → 5.3 mAV_s = 12 V, I_s = 3 mA

I = mA

5.Hard

Use superposition to find the voltage V_R3 across R₃ with the polarity shown.

V₁ = 10 VI_s = 0.5 AV₂ = 36 VR₁ = 15 ΩR₂ = 20 ΩR₃ = 20 ΩR₄ = 15 Ω

V_R3 = V

6.Hard

Use superposition to find the power P_R2 absorbed by R₂.

V₁ = 5 VI_s = 6 AV₂ = 36 VR₁ = 3 ΩR₂ = 8 ΩR₃ = 25 ΩR₄ = 25 Ω

P_R2 = W

Answer key

1. I = 20 mA
2. I_R1′ = 1.875 A
3. I_R2 = −0.1429 A
4. I = 7.5 mA
5. V_R3 = −1.016 V
6. P_R2 = 207.1 W

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