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​ = 20 VV2​ = 6 VIRL​

A linear resistive circuit contains two independent voltage sources, V1 = 20 V and V2 = 6 V. With both sources on, the current through the load resistor is I = 7.5 mA. With V2 switched off (replaced by a short circuit) and V1 unchanged, the load current is −2 mA. Find the load current I when V1 is raised to 40 V and V2 stays at 6 V.

I = 7.5 mA (both sources)I = −2 mA (only V1)
I = mA
2.Easy
R1​ = 5 ΩR2​ = 3 Ω+−V1​15 VR3​2 Ω+−VR3​A+−V2​6 V

Use superposition to find the voltage VR3 across R3 with the polarity shown.

V1 = 15 VV2 = 6 VR1 = 5 ΩR2 = 3 ΩR3 = 2 Ω
VR3 = V
3.Medium
R1​ = 15 ΩR3​ = 12 Ω+−V1​15 VR2​10 ΩAR4​12 Ω−+VR4​BIs​3 A

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

V1 = 15 VIs = 3 AR1 = 15 ΩR2 = 10 ΩR3 = 12 ΩR4 = 12 Ω
VR4 = V
4.Medium
R1​ = 2 ΩIR1​R3​ = 2 Ω+−V1​24 VR2​20 ΩAR4​2 ΩBIs​5 A

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

V1 = 24 VIs = 5 AR1 = 2 ΩR2 = 20 ΩR3 = 2 ΩR4 = 2 Ω
IR1 = A
5.Hard
linear circuitV1​V2​Is​IRL​

A linear resistive circuit contains three independent sources: V1, V2 and Is. The current I through a load is measured three times. With all sources at their normal values, I = 25.5 mA. With V1 doubled and the other two unchanged, I = 35.5 mA. With the direction of Is reversed and the other two unchanged, I = 7.5 mA. Find the load current I when V2 is switched off and V1 and Is have their normal values.

normal: I = 25.5 mA2·V1: I = 35.5 mA−Is: I = 7.5 mA
I = mA
6.Hard
R1​ = 15 ΩR2​ = 10 ΩR4​ = 3 Ω+−V1​9 VR3​30 ΩIR3​AIs​4 AB+−V2​?

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

V1 = 9 VIs = 4 AR1 = 15 ΩR2 = 10 ΩR3 = 30 ΩR4 = 3 Ω
V2 = V

Answer key

  1. 1. I = 5.5 mA
  2. 2. VR3 = 4.839 V
  3. 3. VR4 = 19.2 V
  4. 4. IR1 = 2.938 A
  5. 5. I = 19 mA
  6. 6. V2 = 4.2 V

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