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​ = 3 Ω+−V1​24 VR2​?AIs​1 A

The node voltage at A is measured as VA = 14 V. Use nodal analysis to find the resistance R2.

V1 = 24 VIs = 1 AR1 = 3 ΩVA = 14 V
R2 = Ω
2.Easy
R1​ = 6 ΩR2​ = 5 Ω+−V1​12 VR3​12 ΩA+−V2​20 V

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

V1 = 12 VV2 = 20 VR1 = 6 ΩR2 = 5 ΩR3 = 12 Ω
VA = V
3.Medium
−+Vs​ = 8 VIs​2 AAR1​2 ΩR2​2 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 = 2 AVs = 8 VR1 = 2 ΩR2 = 2 Ω
VB = V
4.Medium
R1​12 Ω−+V1​15 VR2​3 Ω+−V2​6 VR3​6 Ω+−V3​30 VI3​A

Three branches are connected between node A and ground, as shown. Use nodal analysis to find the current I3 in branch 3, flowing up into node A in the direction of the arrow.

V1 = 15 VR1 = 12 ΩV2 = 6 VR2 = 3 ΩV3 = 30 VR3 = 6 Ω
I3 = A
5.Hard
R1​ = 20 ΩR2​ = 5 ΩIR2​R4​ = 8 Ω+−V1​15 VR3​10 ΩAR5​6 ΩBIs​4 A+−V2​30 V

Use nodal analysis to find the current IR2 through R2 in the direction of the arrow.

V1 = 15 VIs = 4 AV2 = 30 VR1 = 20 ΩR2 = 5 ΩR3 = 10 ΩR4 = 8 ΩR5 = 6 Ω
IR2 = A
6.Hard
R1​ = 10 ΩR2​ = 25 ΩR4​ = 6 Ω+−V1​9 VR3​4 ΩAR5​10 ΩBIs​1.5 A−+V2​18 V

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

V1 = 9 VIs = 1.5 AV2 = 18 VR1 = 10 ΩR2 = 25 ΩR3 = 4 ΩR4 = 6 ΩR5 = 10 Ω
VB = V

Answer key

  1. 1. R2 = 3.231 Ω
  2. 2. VA = 13.33 V
  3. 3. VB = 6 V
  4. 4. I3 = 3.357 A
  5. 5. IR2 = −1.429 A
  6. 6. VB = −4.653 V

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