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​ = 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 = 22.5 mA. With V2 switched off (replaced by a short circuit) and V1 unchanged, the load current is 12.5 mA. Find the load current I when V1 is switched off and only V2 = 12 V is active.

I = 22.5 mA (both sources)I = 12.5 mA (only V1)
I = mA
2.Easy
R1​ = 4 ΩR2​ = 4 Ω+−V1​12 VR3​8 Ω+−VR3​A+−V2​6 V

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

V1 = 12 VV2 = 6 VR1 = 4 ΩR2 = 4 ΩR3 = 8 Ω
VR3 = V
3.Medium
R1​ = 5 ΩR3​ = 4 ΩIR3​+−V1​10 VR2​3 ΩAR4​15 ΩBIs​5 A

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

V1 = 10 VIs = 5 AR1 = 5 ΩR2 = 3 ΩR3 = 4 ΩR4 = 15 Ω
IR3 = A
4.Medium
R1​ = 10 ΩIR1​R3​ = 8 Ω+−V1​18 VR2​15 ΩAR4​3 ΩBIs​1.5 A

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

V1 = 18 VIs = 1.5 AR1 = 10 ΩR2 = 15 ΩR3 = 8 ΩR4 = 3 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 = 16.5 mA. With V1 doubled and the other two unchanged, I = 21.5 mA. With the direction of Is reversed and the other two unchanged, I = 5.5 mA. Find the load current I when V2 is switched off and V1 and Is have their normal values.

normal: I = 16.5 mA2·V1: I = 21.5 mA−Is: I = 5.5 mA
I = mA
6.Hard
R1​ = 20 ΩR2​ = 15 ΩR4​ = 6 Ω+−V1​15 VR3​4 ΩIR3​AIs​6 AB+−V2​?

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

V1 = 15 VIs = 6 AR1 = 20 ΩR2 = 15 ΩR3 = 4 ΩR4 = 6 Ω
V2 = V

Answer key

  1. 1. I = 10 mA
  2. 2. VR3 = 7.2 V
  3. 3. IR3 = −3.413 A
  4. 4. IR1 = 0.9424 A
  5. 5. I = 10.5 mA
  6. 6. V2 = 20.25 V

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