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​ = 6 ΩR2​ = 3 ΩIR2​+−V1​20 VR3​6 ΩA+−V2​6 V

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

V1 = 20 VV2 = 6 VR1 = 6 ΩR2 = 3 ΩR3 = 6 Ω
IR2 = A
2.Easy
R1​ = 10 ΩIR1​+−V1​10 VR2​12 ΩAIs​2 A

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

V1 = 10 VIs = 2 AR1 = 10 ΩR2 = 12 Ω
IR1 = A
3.Medium
R1​ = 10 ΩR3​ = 20 Ω+−V1​24 VR2​3 ΩAR4​20 ΩBIs​1.5 A

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

V1 = 24 VIs = 1.5 AR1 = 10 ΩR2 = 3 ΩR3 = 20 ΩR4 = 20 Ω
PIs = W
4.Medium
R1​ = 3 ΩR3​ = 2 ΩIR3​+−V1​9 VR2​20 ΩAR4​4 ΩBIs​1.5 A

Use nodal analysis to find the current IR3 through R3 in the direction of the arrow.

V1 = 9 VIs = 1.5 AR1 = 3 ΩR2 = 20 ΩR3 = 2 ΩR4 = 4 Ω
IR3 = A
5.Hard
R1​ = 6 Ω−+Vs​ = 3 V+−V1​9 VR2​12 ΩAR3​5 ΩBIs​2.5 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 node voltage VB (measured from ground).

V1 = 9 VIs = 2.5 AVs = 3 VR1 = 6 ΩR2 = 12 ΩR3 = 5 Ω
VB = V
6.Hard
R1​ = 3 ΩR2​ = 20 ΩR4​ = 6 Ω+−V1​30 VR3​12 ΩAR5​4 ΩBIs​1.5 A+−V2​18 V

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

V1 = 30 VIs = 1.5 AV2 = 18 VR1 = 3 ΩR2 = 20 ΩR3 = 12 ΩR4 = 6 ΩR5 = 4 Ω
VB = V

Answer key

  1. 1. IR2 = 0.6667 A
  2. 2. IR1 = −0.6364 A
  3. 3. PIs = 27.65 W
  4. 4. IR3 = 0.2121 A
  5. 5. VB = 10.56 V
  6. 6. VB = 12.08 V

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