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 Ω+−V1​24 VR2​?AIs​3 A

The node voltage at A is measured as VA = 31.5 V. Use nodal analysis to find the resistance R2.

V1 = 24 VIs = 3 AR1 = 12 ΩVA = 31.5 V
R2 = Ω
2.Easy
R1​ = 4 Ω+−V1​15 VR2​?AIs​2 A

The node voltage at A is measured as VA = 14.5 V. Use nodal analysis to find the resistance R2.

V1 = 15 VIs = 2 AR1 = 4 ΩVA = 14.5 V
R2 = Ω
3.Medium
−+Vs​ = 6 VIs​1 AAR1​8 ΩR2​12 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 = 1 AVs = 6 VR1 = 8 ΩR2 = 12 Ω
VB = V
4.Medium
R1​ = 4 ΩR3​ = 10 ΩIR3​+−V1​6 VR2​4 ΩAR4​4 ΩBIs​2.5 A

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

V1 = 6 VIs = 2.5 AR1 = 4 ΩR2 = 4 ΩR3 = 10 ΩR4 = 4 Ω
IR3 = A
5.Hard
R1​ = 6 ΩIR1​+−Vs​ = 10 V+−V1​12 VR2​12 ΩAR3​6 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 = 12 VIs = 2.5 AVs = 10 VR1 = 6 ΩR2 = 12 ΩR3 = 6 Ω
IR1 = A
6.Hard
R1​ = 4 ΩR3​ = 2 Ω+−V1​36 VR2​6 ΩAR4​5 ΩBIs​?

The current source is adjusted until the node voltage at A is VA = 27 V. Use nodal analysis to find the source current Is (direction as shown).

V1 = 36 VR1 = 4 ΩR2 = 6 ΩR3 = 2 ΩR4 = 5 ΩVA = 27 V
Is = A

Answer key

  1. 1. R2 = 13.26 Ω
  2. 2. R2 = 6.824 Ω
  3. 3. VB = 8.4 V
  4. 4. IR3 = −0.4375 A
  5. 5. IR1 = −0.4667 A
  6. 6. Is = 8.55 A

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