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 = 10 V and V₂ = 15 V. With both sources on, the current through the load resistor is I = 23 mA. With V₂ switched off (replaced by a short circuit) and V₁ unchanged, the load current is 15.5 mA. Find the load current I when V₁ is switched off and only V₂ = 15 V is active.

I = 23 mA (both sources)I = 15.5 mA (only V₁)

I = mA

2.Easy

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

V₁ = 20 VV₂ = 10 VR₁ = 2 ΩR₂ = 8 ΩR₃ = 4 Ω

I_R2 = A

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 = 6 mA, I = 3 mA; with V_s = 20 V and I_s = 2 mA, I = 9 mA. Find the load current I when V_s = 4 V and I_s = 10 mA.

12 V, 6 mA → 3 mA20 V, 2 mA → 9 mAV_s = 4 V, I_s = 10 mA

I = mA

4.Medium

Find the value of the current source I_s (direction as shown) that makes the current I_R3 through R₃ equal to zero.

V₁ = 12 VR₁ = 10 ΩR₂ = 6 ΩR₃ = 4 ΩR₄ = 10 Ω

I_s = A

5.Hard

Use superposition to find the power P_R1 absorbed by R₁.

V₁ = 10 VI_s = 0.5 AV₂ = 15 VR₁ = 10 ΩR₂ = 25 ΩR₃ = 12 ΩR₄ = 12 Ω

P_R1 = W

6.Hard

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

V₁ = 6 VI_s = 4 AR₁ = 15 ΩR₂ = 12 ΩR₃ = 5 ΩR₄ = 2 Ω

V₂ = V

Answer key

1. I = 7.5 mA
2. I_R2 = 0.3571 A
3. I = −3 mA
4. I_s = 0.45 A
5. P_R1 = 4.099 W
6. V₂ = 2.4 V

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