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 ΩIR1​R2​ = 8 Ω+−V1​24 VR3​4 ΩA+−V2​10 V

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

V1 = 24 VV2 = 10 VR1 = 4 ΩR2 = 8 ΩR3 = 4 Ω
IR1 = A
2.Easy
R1​ = 2 Ω+−V1​18 VR2​?AIs​2 A

The node voltage at A is measured as VA = 12.5 V. Use nodal analysis to find the resistance R2.

V1 = 18 VIs = 2 AR1 = 2 ΩVA = 12.5 V
R2 = Ω
3.Medium
R1​ = 2 ΩR3​ = 8 Ω+−V1​6 VR2​6 ΩAR4​8 ΩBIs​1 A

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

V1 = 6 VIs = 1 AR1 = 2 ΩR2 = 6 ΩR3 = 8 ΩR4 = 8 Ω
VA = V
4.Medium
R1​ = 2 ΩR3​ = 8 Ω+−V1​24 VR2​12 ΩAR4​4 ΩBIs​2 A

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

V1 = 24 VIs = 2 AR1 = 2 ΩR2 = 12 ΩR3 = 8 ΩR4 = 4 Ω
PIs = W
5.Hard
R1​ = 4 Ω+−Vs​ = 10 V+−V1​5 VR2​12 ΩAR3​10 ΩBIs​4 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 node voltage VA (measured from ground).

V1 = 5 VIs = 4 AVs = 10 VR1 = 4 ΩR2 = 12 ΩR3 = 10 Ω
VA = V
6.Hard
R1​ = 2 Ω−+Vs​ = 10 V+−V1​36 VR2​8 ΩAR3​10 ΩBIs​1.5 A

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).

V1 = 36 VIs = 1.5 AVs = 10 VR1 = 2 ΩR2 = 8 ΩR3 = 10 Ω
VB = V

Answer key

  1. 1. IR1 = 3.1 A
  2. 2. R2 = 2.632 Ω
  3. 3. VA = 4.8 V
  4. 4. PIs = 23.33 W
  5. 5. VA = 14.42 V
  6. 6. VB = 35.52 V

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