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​ = 10 VV2​ = 10 VIRL​

A linear resistive circuit contains two independent voltage sources, V1 = 10 V and V2 = 10 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 19 mA. Find the load current I when V1 is raised to 20 V and V2 stays at 10 V.

I = 31.5 mA (both sources)I = 19 mA (only V1)
I = mA
2.Easy
R1​ = 2 ΩR2​ = 4 Ω+−V1​20 VR3​4 ΩIR3​A+−V2​10 V

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

V1 = 20 VV2 = 10 VR1 = 2 ΩR2 = 4 ΩR3 = 4 Ω
IR3 = A
3.Medium
R1​ = 3 ΩIR1​R3​ = 10 Ω+−V1​6 VR2​8 ΩAR4​20 ΩBIs​3 A

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

V1 = 6 VIs = 3 AR1 = 3 ΩR2 = 8 ΩR3 = 10 ΩR4 = 20 Ω
IR1 = A
4.Medium
R1​ = 10 ΩR3​ = 8 ΩIR3​+−V1​30 VR2​8 ΩAR4​6 ΩBIs​?

Find the value of the current source Is (direction as shown) that makes the current IR3 through R3 equal to zero.

V1 = 30 VR1 = 10 ΩR2 = 8 ΩR3 = 8 ΩR4 = 6 Ω
Is = 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 = 6.5 mA. With V1 doubled and the other two unchanged, I = 2.5 mA. With the direction of Is reversed and the other two unchanged, I = −12.5 mA. Find the load current I when V2 is switched off and V1 and Is have their normal values.

normal: I = 6.5 mA2·V1: I = 2.5 mA−Is: I = −12.5 mA
I = mA
6.Hard
R1​ = 2 ΩR2​ = 20 ΩR4​ = 4 ΩIR4​+−V1​30 VR3​15 ΩAIs​5 AB+−V2​9 V

Use superposition to find the current IR4 through R4 in the direction of the arrow.

V1 = 30 VIs = 5 AV2 = 9 VR1 = 2 ΩR2 = 20 ΩR3 = 15 ΩR4 = 4 Ω
IR4 = A

Answer key

  1. 1. I = 50.5 mA
  2. 2. IR3 = 3.125 A
  3. 3. IR1 = 0.7119 A
  4. 4. Is = 2.222 A
  5. 5. I = 5.5 mA
  6. 6. IR4 = 4.902 A

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