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​ = 2 ΩIR1​R2​ = 12 Ω+−V1​8 VR3​4 ΩA+−V2​8 V

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

V1 = 8 VV2 = 8 VR1 = 2 ΩR2 = 12 ΩR3 = 4 Ω
IR1 = A
2.Easy
R1​ = 10 Ω+−V1​24 VR2​10 ΩAIs​1 A

Use superposition to find the node voltage VA (measured from ground).

V1 = 24 VIs = 1 AR1 = 10 ΩR2 = 10 Ω
VA = V
3.Medium
R1​ = 8 ΩR3​ = 20 Ω+−V1​6 VR2​2 Ω+−VR2​AR4​6 ΩBIs​3 A

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

V1 = 6 VIs = 3 AR1 = 8 ΩR2 = 2 ΩR3 = 20 ΩR4 = 6 Ω
VR2 = V
4.Medium
R1​ = 3 ΩR3​ = 15 ΩIR3​+−V1​9 VR2​6 ΩAR4​5 ΩBIs​2.5 A

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

V1 = 9 VIs = 2.5 AR1 = 3 ΩR2 = 6 ΩR3 = 15 ΩR4 = 5 Ω
IR3 = A
5.Hard
R1​ = 2 ΩR2​ = 10 ΩR4​ = 8 Ω+−V1​15 VR3​20 Ω−+VR3​AIs​4 AB+−V2​5 V

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

V1 = 15 VIs = 4 AV2 = 5 VR1 = 2 ΩR2 = 10 ΩR3 = 20 ΩR4 = 8 Ω
VR3 = 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 = 1 mA. With V1 doubled and the other two unchanged, I = 2 mA. With the direction of Is reversed and the other two unchanged, I = −8 mA. Find the load current I when V2 is switched off and V1 and Is have their normal values.

normal: I = 1 mA2·V1: I = 2 mA−Is: I = −8 mA
I = mA

Answer key

  1. 1. IR1 = 1.2 A
  2. 2. VA = 17 V
  3. 3. VR2 = 2.174 V
  4. 4. IR3 = 0.2955 A
  5. 5. VR3 = −9.908 V
  6. 6. I = 5.5 mA

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