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 ΩR2​ = 4 Ω+−V1​15 VR3​2 ΩA+−V2​6 V

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

V1 = 15 VV2 = 6 VR1 = 4 ΩR2 = 4 ΩR3 = 2 Ω
VA = V
2.Easy
R1​ = 8 Ω+−V1​8 VR2​5 ΩAIs​2 A

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

V1 = 8 VIs = 2 AR1 = 8 ΩR2 = 5 Ω
PIs = W
3.Medium
R1​ = 8 ΩR3​ = 6 Ω+−V1​10 VR2​20 ΩAR4​12 ΩBIs​3 A

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

V1 = 10 VIs = 3 AR1 = 8 ΩR2 = 20 ΩR3 = 6 ΩR4 = 12 Ω
VB = V
4.Medium
−+Vs​ = 12 VIs​3 AAR1​12 ΩR2​15 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 VA (measured from ground).

Is = 3 AVs = 12 VR1 = 12 ΩR2 = 15 Ω
VA = V
5.Hard
R1​ = 2 ΩR3​ = 3 Ω+−V1​9 VR2​10 ΩAR4​6 ΩBIs​?

The current source is adjusted until the node voltage at A is VA = 13 V. Use nodal analysis to find the source current Is (direction as shown).

V1 = 9 VR1 = 2 ΩR2 = 10 ΩR3 = 3 ΩR4 = 6 ΩVA = 13 V
Is = A
6.Hard
R1​ = 3 ΩR2​ = 20 ΩR4​ = 30 ΩIR4​+−V1​9 VR3​12 ΩAR5​8 ΩBIs​6 A+−V2​12 V

Use nodal analysis to find the current IR4 through R4 in the direction of the arrow.

V1 = 9 VIs = 6 AV2 = 12 VR1 = 3 ΩR2 = 20 ΩR3 = 12 ΩR4 = 30 ΩR5 = 8 Ω
IR4 = A

Answer key

  1. 1. VA = 5.25 V
  2. 2. PIs = 18.46 W
  3. 3. VB = −14.17 V
  4. 4. VA = 14.67 V
  5. 5. Is = 7.117 A
  6. 6. IR4 = 0.7038 A

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