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​ = 5 ΩIR1​R2​ = 5 Ω+−V1​12 VR3​12 ΩA+−V2​20 V

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

V1 = 12 VV2 = 20 VR1 = 5 ΩR2 = 5 ΩR3 = 12 Ω
IR1 = A
2.Easy
linear circuitV1​ = 10 VV2​ = 5 VIRL​

A linear resistive circuit contains two independent voltage sources, V1 = 10 V and V2 = 5 V. With both sources on, the current through the load resistor is I = −22 mA. With V2 switched off (replaced by a short circuit) and V1 unchanged, the load current is −6 mA. Find the load current I when V1 is raised to 20 V and V2 stays at 5 V.

I = −22 mA (both sources)I = −6 mA (only V1)
I = mA
3.Medium
R1​ = 3 ΩR3​ = 8 Ω+−V1​15 VR2​3 ΩAR4​2 Ω+−VR4​BIs​3 A

Use superposition to find the voltage VR4 across R4 with the polarity shown.

V1 = 15 VIs = 3 AR1 = 3 ΩR2 = 3 ΩR3 = 8 ΩR4 = 2 Ω
VR4 = V
4.Medium
R1​ = 12 ΩR3​ = 15 Ω+−V1​10 VR2​10 ΩIR2​AR4​3 ΩBIs​1 A

Use superposition to find the current IR2 through R2 in the direction of the arrow.

V1 = 10 VIs = 1 AR1 = 12 ΩR2 = 10 ΩR3 = 15 ΩR4 = 3 Ω
IR2 = A
5.Hard
R1​ = 15 ΩR2​ = 3 ΩR4​ = 5 Ω+−V1​12 VR3​10 ΩIR3​AIs​3 AB+−V2​?

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

V1 = 12 VIs = 3 AR1 = 15 ΩR2 = 3 ΩR3 = 10 ΩR4 = 5 Ω
V2 = V
6.Hard
R1​ = 15 ΩIR1​R2​ = 10 ΩR4​ = 15 Ω+−V1​6 VR3​30 ΩAIs​6 AB−+V2​24 V

Use superposition to find the power PR1 absorbed by R1.

V1 = 6 VIs = 6 AV2 = 24 VR1 = 15 ΩR2 = 10 ΩR3 = 30 ΩR4 = 15 Ω
PR1 = W

Answer key

  1. 1. IR1 = −0.2483 A
  2. 2. I = −28 mA
  3. 3. VR4 = −3.652 V
  4. 4. IR2 = −0.4186 A
  5. 5. V2 = 8.6 V
  6. 6. PR1 = 16.46 W

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