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​6 Ω+−V1​6 VR2​2 Ω+−V2​10 VR3​2 Ω+−V3​24 VA

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

V1 = 6 VR1 = 6 ΩV2 = 10 VR2 = 2 ΩV3 = 24 VR3 = 2 Ω
VA = V
2.Easy
R1​ = 4 Ω+−V1​18 VR2​12 ΩAIs​2 A

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

V1 = 18 VIs = 2 AR1 = 4 ΩR2 = 12 Ω
VA = V
3.Medium
R1​ = 4 ΩR3​ = 5 Ω+−V1​24 VR2​6 ΩAR4​12 ΩBIs​4 A

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

V1 = 24 VIs = 4 AR1 = 4 ΩR2 = 6 ΩR3 = 5 ΩR4 = 12 Ω
VB = V
4.Medium
R1​ = 5 ΩR3​ = 3 Ω+−V1​18 VR2​20 ΩAR4​20 ΩBIs​4 A

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

V1 = 18 VIs = 4 AR1 = 5 ΩR2 = 20 ΩR3 = 3 ΩR4 = 20 Ω
PIs = W
5.Hard
R1​ = 2 ΩR3​ = 12 Ω+−V1​9 VR2​8 ΩAR4​20 ΩBIs​?

The current source is adjusted until the node voltage at A is VA = 12 V. Use nodal analysis to find the source current Is (direction as shown).

V1 = 9 VR1 = 2 ΩR2 = 8 ΩR3 = 12 ΩR4 = 20 ΩVA = 12 V
Is = A
6.Hard
R1​ = 2 Ω−+Vs​ = 3 V+−V1​5 VR2​25 ΩAR3​2 ΩBIs​2.5 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 node voltage VA (measured from ground).

V1 = 5 VIs = 2.5 AVs = 3 VR1 = 2 ΩR2 = 25 ΩR3 = 2 Ω
VA = V

Answer key

  1. 1. VA = 15.43 V
  2. 2. VA = 19.5 V
  3. 3. VB = 27.22 V
  4. 4. PIs = 125.6 W
  5. 5. Is = 5.4 A
  6. 6. VA = 3.365 V

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