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​ = 4 Ω+−V1​20 VR3​12 ΩA+−V2​15 V

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

V1 = 20 VV2 = 15 VR1 = 4 ΩR2 = 4 ΩR3 = 12 Ω
IR1 = A
2.Easy
R1​10 Ω+−V1​18 VR2​12 Ω+−V2​18 VR3​2 ΩA

Three branches are connected between node A and ground, as shown. Use nodal analysis to find the node voltage VA.

V1 = 18 VR1 = 10 ΩV2 = 18 VR2 = 12 ΩR3 = 2 Ω
VA = V
3.Medium
−+Vs​ = 4 VIs​5 AAR1​3 ΩR2​10 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 = 5 AVs = 4 VR1 = 3 ΩR2 = 10 Ω
VB = V
4.Medium
R1​ = 6 ΩR3​ = 4 ΩIR3​+−V1​24 VR2​2 ΩAR4​10 ΩBIs​5 A

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

V1 = 24 VIs = 5 AR1 = 6 ΩR2 = 2 ΩR3 = 4 ΩR4 = 10 Ω
IR3 = A
5.Hard
R1​ = 30 ΩR2​ = 5 ΩIR2​R4​ = 12 Ω+−V1​24 VR3​2 ΩAR5​4 ΩBIs​3 A−+V2​36 V

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

V1 = 24 VIs = 3 AV2 = 36 VR1 = 30 ΩR2 = 5 ΩR3 = 2 ΩR4 = 12 ΩR5 = 4 Ω
IR2 = A
6.Hard
R1​ = 2 ΩIR1​+−Vs​ = 12 V+−V1​36 VR2​25 ΩAR3​20 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 = 36 VIs = 2.5 AVs = 12 VR1 = 2 ΩR2 = 25 ΩR3 = 20 Ω
IR1 = A

Answer key

  1. 1. IR1 = 1.25 A
  2. 2. VA = 4.829 V
  3. 3. VB = 14.62 V
  4. 4. IR3 = −2.839 A
  5. 5. IR2 = 1.975 A
  6. 6. IR1 = 0.1186 A

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