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​5 ΩIR2​AIs​1 A

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

V1 = 20 VIs = 1 AR1 = 8 ΩR2 = 5 Ω
IR2 = A
2.Easy
R1​ = 2 Ω+−V1​8 VR2​?AIs​3 A

The node voltage at A is measured as VA = 9 V. Use nodal analysis to find the resistance R2.

V1 = 8 VIs = 3 AR1 = 2 ΩVA = 9 V
R2 = Ω
3.Medium
R1​ = 3 ΩR3​ = 4 Ω+−V1​10 VR2​6 ΩAR4​12 ΩBIs​2.5 A

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

V1 = 10 VIs = 2.5 AR1 = 3 ΩR2 = 6 ΩR3 = 4 ΩR4 = 12 Ω
VA = V
4.Medium
−+Vs​ = 3 VIs​5 AAR1​20 ΩR2​2 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 VA (measured from ground).

Is = 5 AVs = 3 VR1 = 20 ΩR2 = 2 Ω
VA = V
5.Hard
R1​ = 6 ΩR2​ = 8 ΩR4​ = 10 ΩIR4​+−V1​9 VR3​20 ΩAR5​8 ΩBIs​0.5 A+−V2​30 V

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

V1 = 9 VIs = 0.5 AV2 = 30 VR1 = 6 ΩR2 = 8 ΩR3 = 20 ΩR4 = 10 ΩR5 = 8 Ω
IR4 = A
6.Hard
R1​ = 8 Ω−+Vs​ = 4 V+−V1​30 VR2​8 ΩAR3​30 ΩBIs​6 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 = 30 VIs = 6 AVs = 4 VR1 = 8 ΩR2 = 8 ΩR3 = 30 Ω
VB = V

Answer key

  1. 1. IR2 = 2.154 A
  2. 2. R2 = 3.6 Ω
  3. 3. VA = 9.259 V
  4. 4. VA = 6.364 V
  5. 5. IR4 = −1.998 A
  6. 6. VB = 37.94 V

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