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 = 24 VV₂ = 24 VR₁ = 2 ΩR₂ = 8 ΩR₃ = 2 Ω

I_R3 = A

2.Easy

A linear resistive circuit contains two independent voltage sources, V₁ = 24 V and V₂ = 6 V. With both sources on, the current through the load resistor is I = 17 mA. With V₂ switched off (replaced by a short circuit) and V₁ unchanged, the load current is 13 mA. Find the load current I when V₁ is raised to 48 V and V₂ stays at 6 V.

I = 17 mA (both sources)I = 13 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 = 12 V and I_s = 10 mA, I = 5.8 mA; with V_s = 15 V and I_s = 10 mA, I = 7 mA. Find the load current I when V_s = 20 V and I_s = 1 mA.

12 V, 10 mA → 5.8 mA15 V, 10 mA → 7 mAV_s = 20 V, I_s = 1 mA

I = mA

4.Medium

Use superposition to find the current I_R1 through R₁ in the direction of the arrow.

V₁ = 30 VI_s = 2 AR₁ = 15 ΩR₂ = 6 ΩR₃ = 3 ΩR₄ = 5 Ω

I_R1 = A

5.Hard

Find the value of the voltage source V₂ (polarity as shown) that makes the current I_R3 through R₃ equal to zero.

V₁ = 15 VI_s = 5 AR₁ = 6 ΩR₂ = 2 ΩR₃ = 15 ΩR₄ = 15 Ω

V₂ = V

6.Hard

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

V₁ = 6 VI_s = 2 AV₂ = 18 VR₁ = 12 ΩR₂ = 2 ΩR₃ = 25 ΩR₄ = 10 Ω

V_R3 = V

Answer key

1. I_R3 = 6.667 A
2. I = 30 mA
3. I = 8.1 mA
4. I_R1 = 1.395 A
5. V₂ = 32.5 V
6. V_R3 = 17.74 V

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