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​ = 6 Ω+−V1​24 VR2​?AIs​3 A

The node voltage at A is measured as VA = 27.5 V. Use nodal analysis to find the resistance R2.

V1 = 24 VIs = 3 AR1 = 6 ΩVA = 27.5 V
R2 = Ω
2.Easy
R1​ = 6 ΩIR1​+−V1​8 VR2​5 ΩAIs​2 A

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

V1 = 8 VIs = 2 AR1 = 6 ΩR2 = 5 Ω
IR1 = A
3.Medium
R1​ = 6 ΩR3​ = 10 ΩIR3​+−V1​30 VR2​4 ΩAR4​2 ΩBIs​4 A

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

V1 = 30 VIs = 4 AR1 = 6 ΩR2 = 4 ΩR3 = 10 ΩR4 = 2 Ω
IR3 = A
4.Medium
R1​ = 4 ΩR3​ = 15 Ω+−V1​15 VR2​15 ΩAR4​2 ΩBIs​4 A

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

V1 = 15 VIs = 4 AR1 = 4 ΩR2 = 15 ΩR3 = 15 ΩR4 = 2 Ω
VA = V
5.Hard
R1​ = 30 ΩR2​ = 2 ΩR4​ = 15 ΩIR4​+−V1​6 VR3​30 ΩAR5​15 ΩBIs​1.5 A−+V2​18 V

Use nodal analysis to find the current IR4 through R4 in the direction of the arrow.

V1 = 6 VIs = 1.5 AV2 = 18 VR1 = 30 ΩR2 = 2 ΩR3 = 30 ΩR4 = 15 ΩR5 = 15 Ω
IR4 = A
6.Hard
R1​ = 4 ΩIR1​+−Vs​ = 12 V+−V1​5 VR2​4 ΩAR3​4 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 current IR1 through R1 in the direction of the arrow.

V1 = 5 VIs = 4 AVs = 12 VR1 = 4 ΩR2 = 4 ΩR3 = 4 Ω
IR1 = A

Answer key

  1. 1. R2 = 11.38 Ω
  2. 2. IR1 = −0.1818 A
  3. 3. IR3 = 0.2778 A
  4. 4. VA = 8.734 V
  5. 5. IR4 = 1.365 A
  6. 6. IR1 = −1.5 A

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