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​ = 2 ΩR2​ = 4 Ω+−V1​8 VR3​6 Ω+−VR3​A+−V2​15 V

Use superposition to find the contribution VR3′ of V1 alone to the voltage VR3 across R3 with the polarity shown.

V1 = 8 VV2 = 15 VR1 = 2 ΩR2 = 4 ΩR3 = 6 Ω
VR3′ = V
2.Easy
linear circuitV1​ = 15 VV2​ = 20 VIRL​

A linear resistive circuit contains two independent voltage sources, V1 = 15 V and V2 = 20 V. With both sources on, the current through the load resistor is I = −1.5 mA. With V2 switched off (replaced by a short circuit) and V1 unchanged, the load current is −9 mA. Find the load current I when V1 is raised to 30 V and V2 stays at 20 V.

I = −1.5 mA (both sources)I = −9 mA (only V1)
I = mA
3.Medium
R1​ = 6 ΩR3​ = 20 Ω+−V1​30 VR2​20 ΩIR2​AR4​12 ΩBIs​3 A

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

V1 = 30 VIs = 3 AR1 = 6 ΩR2 = 20 ΩR3 = 20 ΩR4 = 12 Ω
IR2 = A
4.Medium
R1​ = 20 ΩR3​ = 20 Ω+−V1​6 VR2​4 ΩAR4​15 Ω−+VR4​BIs​5 A

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

V1 = 6 VIs = 5 AR1 = 20 ΩR2 = 4 ΩR3 = 20 ΩR4 = 15 Ω
VR4 = V
5.Hard
R1​ = 12 ΩR2​ = 10 ΩR4​ = 8 Ω+−V1​10 VR3​25 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 = 10 VIs = 3 AR1 = 12 ΩR2 = 10 ΩR3 = 25 ΩR4 = 8 Ω
V2 = V
6.Hard
R1​ = 8 ΩR2​ = 5 ΩR4​ = 5 ΩIR4​+−V1​30 VR3​10 ΩAIs​2 AB−+V2​36 V

Use superposition to find the power PR4 absorbed by R4.

V1 = 30 VIs = 2 AV2 = 36 VR1 = 8 ΩR2 = 5 ΩR3 = 10 ΩR4 = 5 Ω
PR4 = W

Answer key

  1. 1. VR3′ = 4.364 V
  2. 2. I = −10.5 mA
  3. 3. IR2 = 1.235 A
  4. 4. VR4 = 45.26 V
  5. 5. V2 = 9 V
  6. 6. PR4 = 27.34 W

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