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​2 Ω+−V1​15 VR2​8 Ω+−V2​12 VR3​12 Ω+−V3​6 VA

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

V1 = 15 VR1 = 2 ΩV2 = 12 VR2 = 8 ΩV3 = 6 VR3 = 12 Ω
VA = V
2.Easy
R1​ = 5 Ω+−V1​12 VR2​?AIs​3 A

The node voltage at A is measured as VA = 22 V. Use nodal analysis to find the resistance R2.

V1 = 12 VIs = 3 AR1 = 5 ΩVA = 22 V
R2 = Ω
3.Medium
R1​ = 4 ΩR3​ = 15 Ω+−V1​10 VR2​12 ΩAR4​6 ΩBIs​1 A

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

V1 = 10 VIs = 1 AR1 = 4 ΩR2 = 12 ΩR3 = 15 ΩR4 = 6 Ω
PIs = W
4.Medium
−+Vs​ = 5 VIs​5 AAR1​5 ΩR2​3 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 = 5 AVs = 5 VR1 = 5 ΩR2 = 3 Ω
VB = V
5.Hard
R1​ = 3 ΩR2​ = 2 ΩR4​ = 3 Ω+−V1​10 VR3​30 ΩAR5​8 ΩBIs​2.5 A+−V2​9 V

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

V1 = 10 VIs = 2.5 AV2 = 9 VR1 = 3 ΩR2 = 2 ΩR3 = 30 ΩR4 = 3 ΩR5 = 8 Ω
VB = V
6.Hard
R1​ = 8 ΩIR1​R2​ = 30 ΩR4​ = 30 Ω+−V1​5 VR3​6 ΩAR5​15 ΩBIs​2.5 A+−V2​12 V

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

V1 = 5 VIs = 2.5 AV2 = 12 VR1 = 8 ΩR2 = 30 ΩR3 = 6 ΩR4 = 30 ΩR5 = 15 Ω
IR1 = A

Answer key

  1. 1. VA = 13.41 V
  2. 2. R2 = 22 Ω
  3. 3. PIs = 6.375 W
  4. 4. VB = 11.25 V
  5. 5. VB = 11.08 V
  6. 6. IR1 = 0.09211 A

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