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​ = 5 Ω+−V1​15 VR2​12 ΩAIs​1 A

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

V1 = 15 VIs = 1 AR1 = 5 ΩR2 = 12 Ω
PIs = W
2.Easy
R1​ = 3 ΩR2​ = 2 Ω+−V1​10 VR3​10 ΩA+−V2​6 V

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

V1 = 10 VV2 = 6 VR1 = 3 ΩR2 = 2 ΩR3 = 10 Ω
VA = V
3.Medium
R1​ = 20 ΩR3​ = 5 ΩIR3​+−V1​30 VR2​8 ΩAR4​15 ΩBIs​4 A

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

V1 = 30 VIs = 4 AR1 = 20 ΩR2 = 8 ΩR3 = 5 ΩR4 = 15 Ω
IR3 = A
4.Medium
R1​ = 4 ΩIR1​R3​ = 15 Ω+−V1​15 VR2​4 ΩAR4​2 ΩBIs​2.5 A

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

V1 = 15 VIs = 2.5 AR1 = 4 ΩR2 = 4 ΩR3 = 15 ΩR4 = 2 Ω
IR1 = A
5.Hard
R1​ = 6 ΩR3​ = 4 Ω+−V1​9 VR2​3 ΩAR4​10 ΩBIs​?

The current source is adjusted until the node voltage at A is VA = 9.5 V. Use nodal analysis to find the source current Is (direction as shown).

V1 = 9 VR1 = 6 ΩR2 = 3 ΩR3 = 4 ΩR4 = 10 ΩVA = 9.5 V
Is = A
6.Hard
R1​ = 8 ΩIR1​−+Vs​ = 3 V+−V1​9 VR2​5 ΩAR3​2 ΩBIs​5 A

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 current IR1 through R1 in the direction of the arrow.

V1 = 9 VIs = 5 AVs = 3 VR1 = 8 ΩR2 = 5 ΩR3 = 2 Ω
IR1 = A

Answer key

  1. 1. PIs = 14.12 W
  2. 2. VA = 6.786 V
  3. 3. IR3 = −2 A
  4. 4. IR1 = 1.941 A
  5. 5. Is = 5.5 A
  6. 6. IR1 = 0.4242 A

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