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​24 VR2​3 ΩAIs​2 A

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

V1 = 24 VIs = 2 AR1 = 2 ΩR2 = 3 Ω
PIs = W
2.Easy
R1​ = 2 Ω+−V1​12 VR2​5 ΩAIs​3 A

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

V1 = 12 VIs = 3 AR1 = 2 ΩR2 = 5 Ω
VA = V
3.Medium
−+Vs​ = 3 VIs​1.5 AAR1​15 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 VA (measured from ground).

Is = 1.5 AVs = 3 VR1 = 15 ΩR2 = 8 Ω
VA = V
4.Medium
R1​ = 4 ΩIR1​R3​ = 6 Ω+−V1​12 VR2​6 ΩAR4​15 ΩBIs​3 A

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

V1 = 12 VIs = 3 AR1 = 4 ΩR2 = 6 ΩR3 = 6 ΩR4 = 15 Ω
IR1 = A
5.Hard
R1​ = 8 ΩR2​ = 8 ΩR4​ = 20 ΩIR4​+−V1​5 VR3​12 ΩAR5​5 ΩBIs​0.5 A+−V2​24 V

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

V1 = 5 VIs = 0.5 AV2 = 24 VR1 = 8 ΩR2 = 8 ΩR3 = 12 ΩR4 = 20 ΩR5 = 5 Ω
IR4 = A
6.Hard
R1​ = 4 Ω+−Vs​ = 4 V+−V1​12 VR2​12 ΩAR3​15 ΩBIs​2.5 A

The voltage source Vₛ between A and B has its + terminal at A, so it makes VA − VB = Vₛ. Use nodal analysis with a supernode to find the node voltage VB (measured from ground).

V1 = 12 VIs = 2.5 AVs = 4 VR1 = 4 ΩR2 = 12 ΩR3 = 15 Ω
VB = V

Answer key

  1. 1. PIs = 33.6 W
  2. 2. VA = 12.86 V
  3. 3. VA = 5.87 V
  4. 4. IR1 = 0.2308 A
  5. 5. IR4 = −0.9052 A
  6. 6. VB = 10.42 V

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