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​8 VR2​?AIs​2 A

The node voltage at A is measured as VA = 14.5 V. Use nodal analysis to find the resistance R2.

V1 = 8 VIs = 2 AR1 = 4 ΩVA = 14.5 V
R2 = Ω
2.Easy
R1​ = 6 Ω+−V1​12 VR2​6 ΩAIs​3 A

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

V1 = 12 VIs = 3 AR1 = 6 ΩR2 = 6 Ω
PIs = W
3.Medium
R1​8 Ω+−V1​18 VI1​R2​4 Ω+−V2​10 VR3​8 Ω+−V3​10 VA

Three branches are connected between node A and ground, as shown. Use nodal analysis to find the current I1 in branch 1, flowing up into node A in the direction of the arrow.

V1 = 18 VR1 = 8 ΩV2 = 10 VR2 = 4 ΩV3 = 10 VR3 = 8 Ω
I1 = A
4.Medium
−+Vs​ = 5 VIs​1.5 AAR1​20 ΩR2​8 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 = 1.5 AVs = 5 VR1 = 20 ΩR2 = 8 Ω
VB = V
5.Hard
R1​ = 25 ΩR2​ = 4 ΩR4​ = 5 Ω+−V1​6 VR3​6 ΩAR5​6 ΩBIs​6 A+−V2​15 V

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

V1 = 6 VIs = 6 AV2 = 15 VR1 = 25 ΩR2 = 4 ΩR3 = 6 ΩR4 = 5 ΩR5 = 6 Ω
VA = V
6.Hard
R1​ = 8 ΩIR1​R2​ = 20 ΩR4​ = 15 Ω+−V1​12 VR3​3 ΩAR5​3 ΩBIs​1.5 A−+V2​36 V

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

V1 = 12 VIs = 1.5 AV2 = 36 VR1 = 8 ΩR2 = 20 ΩR3 = 3 ΩR4 = 15 ΩR5 = 3 Ω
IR1 = A

Answer key

  1. 1. R2 = 38.67 Ω
  2. 2. PIs = 45 W
  3. 3. I1 = 0.75 A
  4. 4. VB = 10 V
  5. 5. VA = 10.94 V
  6. 6. IR1 = 1.235 A

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