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​ = 4 ΩIR1​R2​ = 6 Ω+−V1​20 VR3​12 ΩA+−V2​12 V

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

V1 = 20 VV2 = 12 VR1 = 4 ΩR2 = 6 ΩR3 = 12 Ω
IR1 = A
2.Easy
linear circuitV1​ = 24 VV2​ = 12 VIRL​

A linear resistive circuit contains two independent voltage sources, V1 = 24 V and V2 = 12 V. With both sources on, the current through the load resistor is I = 31.5 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 48 V and V2 stays at 12 V.

I = 31.5 mA (both sources)I = 12 mA (only V1)
I = mA
3.Medium
R1​ = 5 ΩR3​ = 3 Ω+−V1​15 VR2​4 Ω+−VR2​AR4​3 ΩBIs​3 A

Use superposition to find the voltage VR2 across R2 with the polarity shown.

V1 = 15 VIs = 3 AR1 = 5 ΩR2 = 4 ΩR3 = 3 ΩR4 = 3 Ω
VR2 = V
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 = 15 V and Is = 3 mA, I = 3.75 mA; with Vs = 20 V and Is = 2 mA, I = 6.5 mA. Find the load current I when Vs = 10 V and Is = 8 mA.

15 V, 3 mA → 3.75 mA20 V, 2 mA → 6.5 mAVs = 10 V, Is = 8 mA
I = mA
5.Hard
R1​ = 10 ΩR2​ = 15 ΩR4​ = 30 Ω+−V1​6 VR3​5 ΩIR3​AIs​2 AB+−V2​?

Find the value of the voltage source V2 (polarity as shown) that makes the current IR3 through R3 equal to zero.

V1 = 6 VIs = 2 AR1 = 10 ΩR2 = 15 ΩR3 = 5 ΩR4 = 30 Ω
V2 = V
6.Hard
R1​ = 20 ΩR2​ = 30 ΩR4​ = 8 Ω+−V1​15 VR3​15 ΩIR3​AIs​6 AB+−V2​24 V

Use superposition to find the current IR3 through R3 in the direction of the arrow.

V1 = 15 VIs = 6 AV2 = 24 VR1 = 20 ΩR2 = 30 ΩR3 = 15 ΩR4 = 8 Ω
IR3 = A

Answer key

  1. 1. IR1 = 1.5 A
  2. 2. I = 43.5 mA
  3. 3. VR2 = 7.297 V
  4. 4. I = −2 mA
  5. 5. V2 = 33 V
  6. 6. IR3 = −1.233 A

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