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​10 VR2​4 ΩAIs​3 A

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

V1 = 10 VIs = 3 AR1 = 4 ΩR2 = 4 Ω
VA = V
2.Easy
R1​ = 12 ΩIR1​+−V1​20 VR2​6 ΩAIs​1 A

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

V1 = 20 VIs = 1 AR1 = 12 ΩR2 = 6 Ω
IR1 = A
3.Medium
R1​ = 5 ΩR3​ = 15 Ω+−V1​9 VR2​12 ΩAR4​2 ΩBIs​2 A

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

V1 = 9 VIs = 2 AR1 = 5 ΩR2 = 12 ΩR3 = 15 ΩR4 = 2 Ω
VB = V
4.Medium
R1​ = 4 ΩR3​ = 4 Ω+−V1​12 VR2​8 ΩAR4​6 ΩBIs​2.5 A

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

V1 = 12 VIs = 2.5 AR1 = 4 ΩR2 = 8 ΩR3 = 4 ΩR4 = 6 Ω
PIs = W
5.Hard
R1​ = 6 Ω+−Vs​ = 4 VIx​+−V1​30 VR2​5 ΩAR3​3 ΩBIs​1 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 current Ix through the voltage source, from A to B as shown by the arrow.

V1 = 30 VIs = 1 AVs = 4 VR1 = 6 ΩR2 = 5 ΩR3 = 3 Ω
Ix = A
6.Hard
R1​ = 6 ΩIR1​−+Vs​ = 4 V+−V1​5 VR2​2 ΩAR3​8 ΩBIs​1 A

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 current IR1 through R1 in the direction of the arrow.

V1 = 5 VIs = 1 AVs = 4 VR1 = 6 ΩR2 = 2 ΩR3 = 8 Ω
IR1 = A

Answer key

  1. 1. VA = 11 V
  2. 2. IR1 = 0.7778 A
  3. 3. VB = 4.229 V
  4. 4. PIs = 29.21 W
  5. 5. Ix = 1.159 A
  6. 6. IR1 = 0.5526 A

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