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​ = 9 VV2​ = 20 VIRL​

A linear resistive circuit contains two independent voltage sources, V1 = 9 V and V2 = 20 V. With both sources on, the current through the load resistor is I = 13 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 raised to 18 V and V2 stays at 20 V.

I = 13 mA (both sources)I = 7 mA (only V1)
I = mA
2.Easy
R1​ = 10 ΩR2​ = 2 Ω+−V1​10 VR3​2 ΩIR3​A+−V2​20 V

Use superposition to find the contribution IR3″ of V2 alone to the current IR3 through R3 in the direction of the arrow.

V1 = 10 VV2 = 20 VR1 = 10 ΩR2 = 2 ΩR3 = 2 Ω
IR3″ = A
3.Medium
R1​ = 6 ΩR3​ = 3 ΩIR3​+−V1​9 VR2​3 ΩAR4​4 ΩBIs​5 A

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

V1 = 9 VIs = 5 AR1 = 6 ΩR2 = 3 ΩR3 = 3 ΩR4 = 4 Ω
IR3 = A
4.Medium
R1​ = 6 ΩR3​ = 10 Ω+−V1​9 VR2​4 Ω+−VR2​AR4​3 ΩBIs​1.5 A

Use superposition to find the voltage VR2 across R2 with the polarity shown.

V1 = 9 VIs = 1.5 AR1 = 6 ΩR2 = 4 ΩR3 = 10 ΩR4 = 3 Ω
VR2 = V
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 = 8 mA. With V1 doubled and the other two unchanged, I = 12.5 mA. With the direction of Is reversed and the other two unchanged, I = −16 mA. Find the load current I when V2 is switched off and V1 and Is have their normal values.

normal: I = 8 mA2·V1: I = 12.5 mA−Is: I = −16 mA
I = mA
6.Hard
R1​ = 25 ΩR2​ = 30 ΩR4​ = 12 ΩIR4​+−V1​36 VR3​12 ΩAIs​1 AB+−V2​24 V

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

V1 = 36 VIs = 1 AV2 = 24 VR1 = 25 ΩR2 = 30 ΩR3 = 12 ΩR4 = 12 Ω
IR4 = A

Answer key

  1. 1. I = 20 mA
  2. 2. IR3″ = 4.545 A
  3. 3. IR3 = 2.556 A
  4. 4. VR2 = 3.74 V
  5. 5. I = 16.5 mA
  6. 6. IR4 = 0.5146 A

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