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​ = 3 Ω+−V1​8 VR2​?AIs​1 A

The node voltage at A is measured as VA = 5 V. Use nodal analysis to find the resistance R2.

V1 = 8 VIs = 1 AR1 = 3 ΩVA = 5 V
R2 = Ω
2.Easy
R1​ = 4 ΩIR1​R2​ = 2 Ω+−V1​10 VR3​6 ΩA+−V2​20 V

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

V1 = 10 VV2 = 20 VR1 = 4 ΩR2 = 2 ΩR3 = 6 Ω
IR1 = A
3.Medium
R1​ = 2 ΩR3​ = 4 Ω+−V1​9 VR2​20 ΩAR4​2 ΩBIs​4 A

Use nodal analysis to find the power PIs delivered by the current source Is.

V1 = 9 VIs = 4 AR1 = 2 ΩR2 = 20 ΩR3 = 4 ΩR4 = 2 Ω
PIs = W
4.Medium
−+Vs​ = 3 VIs​1 AAR1​20 ΩR2​6 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 = 3 VR1 = 20 ΩR2 = 6 Ω
VB = V
5.Hard
R1​ = 5 ΩR2​ = 12 ΩR4​ = 5 Ω+−V1​5 VR3​6 ΩAR5​6 ΩBIs​1 A+−V2​36 V

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

V1 = 5 VIs = 1 AV2 = 36 VR1 = 5 ΩR2 = 12 ΩR3 = 6 ΩR4 = 5 ΩR5 = 6 Ω
VA = V
6.Hard
R1​ = 15 ΩR3​ = 12 Ω+−V1​36 VR2​5 ΩAR4​25 ΩBIs​?

The current source is adjusted until the node voltage at A is VA = 29.5 V. Use nodal analysis to find the source current Is (direction as shown).

V1 = 36 VR1 = 15 ΩR2 = 5 ΩR3 = 12 ΩR4 = 25 ΩVA = 29.5 V
Is = A

Answer key

  1. 1. R2 = 2.5 Ω
  2. 2. IR1 = −0.9091 A
  3. 3. PIs = 32.19 W
  4. 4. VB = 5.308 V
  5. 5. VA = 4.943 V
  6. 6. Is = 9.271 A

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