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​ = 5 Ω+−V1​20 VR2​?AIs​2 A

The node voltage at A is measured as VA = 10 V. Use nodal analysis to find the resistance R2.

V1 = 20 VIs = 2 AR1 = 5 ΩVA = 10 V
R2 = Ω
2.Easy
R1​ = 10 Ω+−V1​6 VR2​5 ΩAIs​1 A

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

V1 = 6 VIs = 1 AR1 = 10 ΩR2 = 5 Ω
PIs = W
3.Medium
R1​ = 10 ΩIR1​R3​ = 10 Ω+−V1​10 VR2​4 ΩAR4​4 ΩBIs​1 A

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

V1 = 10 VIs = 1 AR1 = 10 ΩR2 = 4 ΩR3 = 10 ΩR4 = 4 Ω
IR1 = A
4.Medium
R1​ = 12 ΩR3​ = 6 Ω+−V1​6 VR2​5 ΩAR4​2 ΩBIs​3 A

Use nodal analysis to find the node voltage VB (measured from ground).

V1 = 6 VIs = 3 AR1 = 12 ΩR2 = 5 ΩR3 = 6 ΩR4 = 2 Ω
VB = V
5.Hard
R1​ = 6 ΩR2​ = 30 ΩIR2​R4​ = 8 Ω+−V1​18 VR3​8 ΩAR5​20 ΩBIs​0.5 A+−V2​9 V

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

V1 = 18 VIs = 0.5 AV2 = 9 VR1 = 6 ΩR2 = 30 ΩR3 = 8 ΩR4 = 8 ΩR5 = 20 Ω
IR2 = A
6.Hard
R1​ = 25 ΩR3​ = 10 Ω+−V1​18 VR2​4 ΩAR4​25 ΩBIs​?

The current source is adjusted until the node voltage at A is VA = 12 V. Use nodal analysis to find the source current Is (direction as shown).

V1 = 18 VR1 = 25 ΩR2 = 4 ΩR3 = 10 ΩR4 = 25 ΩVA = 12 V
Is = A

Answer key

  1. 1. R2 = 2.5 Ω
  2. 2. PIs = 5.333 W
  3. 3. IR1 = 0.6949 A
  4. 4. VB = 5.265 V
  5. 5. IR2 = 0.1715 A
  6. 6. Is = 4.344 A

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