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​ = 12 ΩR2​ = 12 Ω+−V1​10 VR3​8 ΩA+−V2​15 V

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

V1 = 10 VV2 = 15 VR1 = 12 ΩR2 = 12 ΩR3 = 8 Ω
VA = V
2.Easy
R1​ = 5 ΩR2​ = 4 Ω+−V1​15 VR3​8 ΩIR3​A+−V2​15 V

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

V1 = 15 VV2 = 15 VR1 = 5 ΩR2 = 4 ΩR3 = 8 Ω
IR3 = A
3.Medium
−+Vs​ = 9 VIs​2 AAR1​20 ΩR2​3 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 = 2 AVs = 9 VR1 = 20 ΩR2 = 3 Ω
VB = V
4.Medium
−+Vs​ = 4 VIs​5 AAR1​15 ΩR2​20 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 = 4 VR1 = 15 ΩR2 = 20 Ω
VA = V
5.Hard
R1​ = 4 ΩR2​ = 25 ΩR4​ = 10 ΩIR4​+−V1​15 VR3​10 ΩAR5​12 ΩBIs​6 A+−V2​18 V

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

V1 = 15 VIs = 6 AV2 = 18 VR1 = 4 ΩR2 = 25 ΩR3 = 10 ΩR4 = 10 ΩR5 = 12 Ω
IR4 = A
6.Hard
R1​ = 12 ΩIR1​+−Vs​ = 4 V+−V1​24 VR2​20 ΩAR3​3 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 = 24 VIs = 2.5 AVs = 4 VR1 = 12 ΩR2 = 20 ΩR3 = 3 Ω
IR1 = A

Answer key

  1. 1. VA = 7.143 V
  2. 2. IR3 = 1.467 A
  3. 3. VB = 6.391 V
  4. 4. VA = 41.14 V
  5. 5. IR4 = 1.933 A
  6. 6. IR1 = 0.9583 A

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