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 Ω+−V1​12 VR2​6 ΩAIs​1 A

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

V1 = 12 VIs = 1 AR1 = 4 ΩR2 = 6 Ω
PIs = W
2.Easy
R1​ = 6 Ω+−V1​15 VR2​?AIs​1 A

The node voltage at A is measured as VA = 3 V. Use nodal analysis to find the resistance R2.

V1 = 15 VIs = 1 AR1 = 6 ΩVA = 3 V
R2 = Ω
3.Medium
R1​ = 5 ΩR3​ = 20 ΩIR3​+−V1​9 VR2​20 ΩAR4​3 ΩBIs​4 A

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

V1 = 9 VIs = 4 AR1 = 5 ΩR2 = 20 ΩR3 = 20 ΩR4 = 3 Ω
IR3 = A
4.Medium
−+Vs​ = 8 VIs​1 AAR1​6 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 = 1 AVs = 8 VR1 = 6 ΩR2 = 20 Ω
VA = V
5.Hard
R1​ = 8 ΩR3​ = 3 Ω+−V1​36 VR2​6 ΩAR4​25 ΩBIs​?

The current source is adjusted until the node voltage at A is VA = 23 V. Use nodal analysis to find the source current Is (direction as shown).

V1 = 36 VR1 = 8 ΩR2 = 6 ΩR3 = 3 ΩR4 = 25 ΩVA = 23 V
Is = A
6.Hard
R1​ = 25 ΩIR1​+−Vs​ = 12 V+−V1​6 VR2​4 ΩAR3​4 ΩBIs​4 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 = 6 VIs = 4 AVs = 12 VR1 = 25 ΩR2 = 4 ΩR3 = 4 Ω
IR1 = A

Answer key

  1. 1. PIs = 9.6 W
  2. 2. R2 = 1 Ω
  3. 3. IR3 = −0.1778 A
  4. 4. VA = 2.769 V
  5. 5. Is = 3.393 A
  6. 6. IR1 = −0.2963 A

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