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​ = 15 VV2​ = 12 VIRL​

A linear resistive circuit contains two independent voltage sources, V1 = 15 V and V2 = 12 V. With both sources on, the current through the load resistor is I = 18.5 mA. With V2 switched off (replaced by a short circuit) and V1 unchanged, the load current is 9.5 mA. Find the load current I when V1 is raised to 30 V and V2 stays at 12 V.

I = 18.5 mA (both sources)I = 9.5 mA (only V1)
I = mA
2.Easy
R1​ = 4 ΩR2​ = 10 ΩIR2​+−V1​15 VR3​12 ΩA+−V2​20 V

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

V1 = 15 VV2 = 20 VR1 = 4 ΩR2 = 10 ΩR3 = 12 Ω
IR2 = A
3.Medium
R1​ = 5 ΩR3​ = 5 ΩIR3​+−V1​24 VR2​4 ΩAR4​4 ΩBIs​?

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

V1 = 24 VR1 = 5 ΩR2 = 4 ΩR3 = 5 ΩR4 = 4 Ω
Is = A
4.Medium
R1​ = 3 ΩR3​ = 20 Ω+−V1​24 VR2​4 Ω+−VR2​AR4​8 ΩBIs​5 A

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

V1 = 24 VIs = 5 AR1 = 3 ΩR2 = 4 ΩR3 = 20 ΩR4 = 8 Ω
VR2 = V
5.Hard
R1​ = 25 ΩR2​ = 25 ΩR4​ = 20 Ω+−V1​15 VR3​2 ΩIR3​AIs​2 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 = 2 AR1 = 25 ΩR2 = 25 ΩR3 = 2 ΩR4 = 20 Ω
V2 = V
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 = −0.5 mA. With V1 doubled and the other two unchanged, I = −3.5 mA. With the direction of Is reversed and the other two unchanged, I = −20.5 mA. Find the load current I when V2 is switched off and V1 and Is have their normal values.

normal: I = −0.5 mA2·V1: I = −3.5 mA−Is: I = −20.5 mA
I = mA

Answer key

  1. 1. I = 28 mA
  2. 2. IR2 = −0.6731 A
  3. 3. Is = 2.667 A
  4. 4. VR2 = 15.23 V
  5. 5. V2 = 13 V
  6. 6. I = 7 mA

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