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​ = 20 VV2​ = 24 VIRL​

A linear resistive circuit contains two independent voltage sources, V1 = 20 V and V2 = 24 V. With both sources on, the current through the load resistor is I = 27 mA. With V2 switched off (replaced by a short circuit) and V1 unchanged, the load current is 7.5 mA. Find the load current I when V1 is raised to 40 V and V2 stays at 24 V.

I = 27 mA (both sources)I = 7.5 mA (only V1)
I = mA
2.Easy
R1​ = 3 Ω+−V1​12 VR2​10 ΩAIs​1 A

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

V1 = 12 VIs = 1 AR1 = 3 ΩR2 = 10 Ω
VA = V
3.Medium
R1​ = 3 ΩR3​ = 6 ΩIR3​+−V1​30 VR2​12 ΩAR4​10 ΩBIs​?

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

V1 = 30 VR1 = 3 ΩR2 = 12 ΩR3 = 6 ΩR4 = 10 Ω
Is = A
4.Medium
R1​ = 12 ΩR3​ = 2 Ω+−V1​18 VR2​5 Ω+−VR2​AR4​12 ΩBIs​4 A

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

V1 = 18 VIs = 4 AR1 = 12 ΩR2 = 5 ΩR3 = 2 ΩR4 = 12 Ω
VR2 = V
5.Hard
R1​ = 30 ΩR2​ = 8 ΩR4​ = 6 ΩIR4​+−V1​9 VR3​15 ΩAIs​5 AB+−V2​18 V

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

V1 = 9 VIs = 5 AV2 = 18 VR1 = 30 ΩR2 = 8 ΩR3 = 15 ΩR4 = 6 Ω
IR4 = 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 = 16 mA. With V1 doubled and the other two unchanged, I = 10.5 mA. With the direction of Is reversed and the other two unchanged, I = −5 mA. Find the load current I when V2 is switched off and V1 and Is have their normal values.

normal: I = 16 mA2·V1: I = 10.5 mA−Is: I = −5 mA
I = mA

Answer key

  1. 1. I = 34.5 mA
  2. 2. VA = 11.54 V
  3. 3. Is = 2.4 A
  4. 4. VR2 = 13.89 V
  5. 5. IR4 = 4.375 A
  6. 6. I = 5 mA

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