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​ = 4 ΩR2​ = 4 Ω+−V1​18 VR3​3 Ω+−VR3​A+−V2​10 V

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

V1 = 18 VV2 = 10 VR1 = 4 ΩR2 = 4 ΩR3 = 3 Ω
VR3 = V
2.Easy
linear circuitV1​ = 9 VV2​ = 12 VIRL​

A linear resistive circuit contains two independent voltage sources, V1 = 9 V and V2 = 12 V. With both sources on, the current through the load resistor is I = −5.5 mA. With V2 switched off (replaced by a short circuit) and V1 unchanged, the load current is 5 mA. Find the load current I when V1 is switched off and only V2 = 12 V is active.

I = −5.5 mA (both sources)I = 5 mA (only V1)
I = mA
3.Medium
R1​ = 8 ΩR3​ = 20 Ω+−V1​24 VR2​8 ΩIR2​AR4​3 ΩBIs​5 A

Use superposition to find the power PR2 absorbed by R2.

V1 = 24 VIs = 5 AR1 = 8 ΩR2 = 8 ΩR3 = 20 ΩR4 = 3 Ω
PR2 = W
4.Medium
R1​ = 12 ΩR3​ = 15 Ω+−V1​15 VR2​5 ΩAR4​3 ΩIR4​BIs​2 A

Use superposition to find the power PR4 absorbed by R4.

V1 = 15 VIs = 2 AR1 = 12 ΩR2 = 5 ΩR3 = 15 ΩR4 = 3 Ω
PR4 = W
5.Hard
R1​ = 5 ΩR2​ = 20 ΩIR2​R4​ = 15 Ω+−V1​30 VR3​30 ΩAIs​3 AB−+V2​15 V

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

V1 = 30 VIs = 3 AV2 = 15 VR1 = 5 ΩR2 = 20 ΩR3 = 30 ΩR4 = 15 Ω
IR2 = A
6.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 = 21 mA. With V1 doubled and the other two unchanged, I = 32 mA. With the direction of Is reversed and the other two unchanged, I = 13 mA. Find the load current I when V2 is switched off and V1 and Is have their normal values.

normal: I = 21 mA2·V1: I = 32 mA−Is: I = 13 mA
I = mA

Answer key

  1. 1. VR3 = 8.4 V
  2. 2. I = −10.5 mA
  3. 3. PR2 = 19.36 W
  4. 4. PR4 = 6.898 W
  5. 5. IR2 = 0.1091 A
  6. 6. I = 15 mA

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