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​ = 5 VV2​ = 24 VIRL​

A linear resistive circuit contains two independent voltage sources, V1 = 5 V and V2 = 24 V. With both sources on, the current through the load resistor is I = 22 mA. With V2 switched off (replaced by a short circuit) and V1 unchanged, the load current is 12 mA. Find the load current I when V1 is raised to 10 V and V2 stays at 24 V.

I = 22 mA (both sources)I = 12 mA (only V1)
I = mA
2.Easy
R1​ = 5 Ω+−V1​18 VR2​8 ΩAIs​3 A

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

V1 = 18 VIs = 3 AR1 = 5 ΩR2 = 8 Ω
VA = V
3.Medium
R1​ = 15 ΩR3​ = 8 Ω+−V1​30 VR2​10 Ω+−VR2​AR4​2 ΩBIs​5 A

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

V1 = 30 VIs = 5 AR1 = 15 ΩR2 = 10 ΩR3 = 8 ΩR4 = 2 Ω
VR2 = V
4.Medium
R1​ = 2 ΩR3​ = 6 Ω+−V1​18 VR2​4 ΩIR2​AR4​10 ΩBIs​1.5 A

Use superposition to find the power PR2 absorbed by R2.

V1 = 18 VIs = 1.5 AR1 = 2 ΩR2 = 4 ΩR3 = 6 ΩR4 = 10 Ω
PR2 = W
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 = 4 mA. With V1 doubled and the other two unchanged, I = −1 mA. With the direction of Is reversed and the other two unchanged, I = −2 mA. Find the load current I when V2 is switched off and V1 and Is have their normal values.

normal: I = 4 mA2·V1: I = −1 mA−Is: I = −2 mA
I = mA
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 = 21.5 mA. With V1 doubled and the other two unchanged, I = 33 mA. With the direction of Is reversed and the other two unchanged, I = 2.5 mA. Find the load current I when V2 is switched off and V1 and Is have their normal values.

normal: I = 21.5 mA2·V1: I = 33 mA−Is: I = 2.5 mA
I = mA

Answer key

  1. 1. I = 34 mA
  2. 2. VA = 20.31 V
  3. 3. VR2 = 11.25 V
  4. 4. PR2 = 37.4 W
  5. 5. I = −2 mA
  6. 6. I = 21 mA

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