Nodal analysis worksheet with answers

Free printable Nodal analysis 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​ = 8 Ω+−V1​20 VR2​?AIs​3 A

The node voltage at A is measured as VA = 17 V. Use nodal analysis to find the resistance R2.

V1 = 20 VIs = 3 AR1 = 8 ΩVA = 17 V
R2 = Ω
2.Easy
R1​ = 3 ΩR2​ = 12 Ω+−V1​6 VR3​12 ΩIR3​A+−V2​12 V

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

V1 = 6 VV2 = 12 VR1 = 3 ΩR2 = 12 ΩR3 = 12 Ω
IR3 = A
3.Medium
R1​ = 2 ΩR3​ = 20 Ω+−V1​10 VR2​5 ΩAR4​5 ΩBIs​3 A

Use nodal analysis to find the power PIs delivered by the current source Is.

V1 = 10 VIs = 3 AR1 = 2 ΩR2 = 5 ΩR3 = 20 ΩR4 = 5 Ω
PIs = W
4.Medium
R1​ = 6 ΩIR1​R3​ = 15 Ω+−V1​12 VR2​12 ΩAR4​5 ΩBIs​5 A

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

V1 = 12 VIs = 5 AR1 = 6 ΩR2 = 12 ΩR3 = 15 ΩR4 = 5 Ω
IR1 = A
5.Hard
R1​ = 15 ΩR3​ = 5 Ω+−V1​5 VR2​5 ΩAR4​15 ΩBIs​?

The current source is adjusted until the node voltage at A is VA = 9 V. Use nodal analysis to find the source current Is (direction as shown).

V1 = 5 VR1 = 15 ΩR2 = 5 ΩR3 = 5 ΩR4 = 15 ΩVA = 9 V
Is = A
6.Hard
R1​ = 25 ΩR2​ = 10 ΩIR2​R4​ = 25 Ω+−V1​6 VR3​15 ΩAR5​3 ΩBIs​1.5 A+−V2​30 V

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

V1 = 6 VIs = 1.5 AV2 = 30 VR1 = 25 ΩR2 = 10 ΩR3 = 15 ΩR4 = 25 ΩR5 = 3 Ω
IR2 = A

Answer key

  1. 1. R2 = 5.037 Ω
  2. 2. IR3 = 0.5 A
  3. 3. PIs = 40.54 W
  4. 4. IR1 = 1.583 A
  5. 5. Is = 3.356 A
  6. 6. IR2 = 0.1385 A

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