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​ = 5 Ω+−V1​12 VR2​6 ΩAIs​3 A

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

V1 = 12 VIs = 3 AR1 = 5 ΩR2 = 6 Ω
VA = V
2.Easy
R1​ = 2 ΩR2​ = 3 ΩIR2​+−V1​6 VR3​10 ΩA+−V2​15 V

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

V1 = 6 VV2 = 15 VR1 = 2 ΩR2 = 3 ΩR3 = 10 Ω
IR2 = A
3.Medium
R1​ = 3 ΩR3​ = 4 ΩIR3​+−V1​10 VR2​12 ΩAR4​8 ΩBIs​2 A

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

V1 = 10 VIs = 2 AR1 = 3 ΩR2 = 12 ΩR3 = 4 ΩR4 = 8 Ω
IR3 = A
4.Medium
R1​ = 20 ΩR3​ = 15 Ω+−V1​6 VR2​10 ΩAR4​12 ΩBIs​3 A

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

V1 = 6 VIs = 3 AR1 = 20 ΩR2 = 10 ΩR3 = 15 ΩR4 = 12 Ω
PIs = W
5.Hard
R1​ = 8 ΩIR1​+−Vs​ = 3 V+−V1​9 VR2​6 ΩAR3​8 ΩBIs​6 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 IR1 through R1 in the direction of the arrow.

V1 = 9 VIs = 6 AVs = 3 VR1 = 8 ΩR2 = 6 ΩR3 = 8 Ω
IR1 = A
6.Hard
R1​ = 4 ΩR2​ = 8 ΩR4​ = 5 Ω+−V1​12 VR3​4 ΩAR5​8 ΩBIs​4 A+−V2​9 V

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

V1 = 12 VIs = 4 AV2 = 9 VR1 = 4 ΩR2 = 8 ΩR3 = 4 ΩR4 = 5 ΩR5 = 8 Ω
VB = V

Answer key

  1. 1. VA = −1.636 V
  2. 2. IR2 = −2.143 A
  3. 3. IR3 = −0.5556 A
  4. 4. PIs = 71.64 W
  5. 5. IR1 = −1.125 A
  6. 6. VB = −3.765 V

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