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
linear circuitV1​ = 15 VV2​ = 12 VIRL​

A linear resistive circuit contains two independent voltage sources, V1 = 15 V and V2 = 12 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 7 mA. Find the load current I when V1 is switched off and only V2 = 12 V is active.

I = 23 mA (both sources)I = 7 mA (only V1)
I = mA
2.Easy
linear circuitV1​ = 5 VV2​ = 12 VIRL​

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 = −7 mA. With V2 switched off (replaced by a short circuit) and V1 unchanged, the load current is −16 mA. Find the load current I when V1 is raised to 10 V and V2 stays at 12 V.

I = −7 mA (both sources)I = −16 mA (only V1)
I = mA
3.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 = 5 V and Is = 6 mA, I = 1.85 mA; with Vs = 8 V and Is = 3 mA, I = 2.3 mA. Find the load current I when Vs = 10 V and Is = 6 mA.

5 V, 6 mA → 1.85 mA8 V, 3 mA → 2.3 mAVs = 10 V, Is = 6 mA
I = mA
4.Medium
R1​ = 8 ΩIR1​R3​ = 3 Ω+−V1​18 VR2​15 ΩAR4​4 ΩBIs​2.5 A

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

V1 = 18 VIs = 2.5 AR1 = 8 ΩR2 = 15 ΩR3 = 3 ΩR4 = 4 Ω
IR1 = A
5.Hard
R1​ = 12 ΩR2​ = 4 ΩR4​ = 8 Ω+−V1​24 VR3​30 ΩIR3​AIs​6 AB+−V2​?

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

V1 = 24 VIs = 6 AR1 = 12 ΩR2 = 4 ΩR3 = 30 ΩR4 = 8 Ω
V2 = V
6.Hard
R1​ = 2 ΩIR1​R2​ = 5 ΩR4​ = 8 Ω+−V1​18 VR3​8 ΩAIs​1.5 AB+−V2​10 V

Use superposition to find the power PR1 absorbed by R1.

V1 = 18 VIs = 1.5 AV2 = 10 VR1 = 2 ΩR2 = 5 ΩR3 = 8 ΩR4 = 8 Ω
PR1 = W

Answer key

  1. 1. I = 16 mA
  2. 2. I = −23 mA
  3. 3. I = 3.1 mA
  4. 4. IR1 = 1.943 A
  5. 5. V2 = 24 V
  6. 6. PR1 = 3.828 W

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