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​ = 4 Ω+−V1​15 VR2​4 ΩAIs​3 A

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

V1 = 15 VIs = 3 AR1 = 4 ΩR2 = 4 Ω
VA = V
2.Easy
R1​ = 5 Ω+−V1​8 VR2​12 ΩIR2​AIs​1 A

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

V1 = 8 VIs = 1 AR1 = 5 ΩR2 = 12 Ω
IR2 = A
3.Medium
R1​ = 4 ΩIR1​R3​ = 4 Ω+−V1​9 VR2​4 ΩAR4​8 ΩBIs​2 A

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

V1 = 9 VIs = 2 AR1 = 4 ΩR2 = 4 ΩR3 = 4 ΩR4 = 8 Ω
IR1 = A
4.Medium
−+Vs​ = 9 VIs​3 AAR1​3 ΩR2​5 ΩB

The voltage source Vₛ between A and B has its + terminal at B, so it makes VB − VA = Vₛ. Use nodal analysis with a supernode to find the node voltage VB (measured from ground).

Is = 3 AVs = 9 VR1 = 3 ΩR2 = 5 Ω
VB = V
5.Hard
R1​ = 20 ΩIR1​+−Vs​ = 3 V+−V1​18 VR2​2 ΩAR3​8 ΩBIs​2.5 A

The voltage source Vₛ between A and B has its + terminal at A, so it makes VA − VB = Vₛ. Use nodal analysis with a supernode to find the current IR1 through R1 in the direction of the arrow.

V1 = 18 VIs = 2.5 AVs = 3 VR1 = 20 ΩR2 = 2 ΩR3 = 8 Ω
IR1 = A
6.Hard
R1​ = 15 ΩR2​ = 25 ΩR4​ = 2 Ω+−V1​12 VR3​30 ΩAR5​8 ΩBIs​2.5 A+−V2​6 V

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

V1 = 12 VIs = 2.5 AV2 = 6 VR1 = 15 ΩR2 = 25 ΩR3 = 30 ΩR4 = 2 ΩR5 = 8 Ω
VB = V

Answer key

  1. 1. VA = 13.5 V
  2. 2. IR2 = 0.7647 A
  3. 3. IR1 = 0.7143 A
  4. 4. VB = 11.25 V
  5. 5. IR1 = 0.6204 A
  6. 6. VB = 1.115 V

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