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​ = 8 Ω+−V1​18 VR2​10 ΩIR2​AIs​3 A

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

V1 = 18 VIs = 3 AR1 = 8 ΩR2 = 10 Ω
IR2 = A
2.Easy
R1​ = 4 ΩIR1​R2​ = 5 Ω+−V1​10 VR3​12 ΩA+−V2​20 V

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

V1 = 10 VV2 = 20 VR1 = 4 ΩR2 = 5 ΩR3 = 12 Ω
IR1 = A
3.Medium
R1​ = 4 ΩR3​ = 20 ΩIR3​+−V1​24 VR2​6 ΩAR4​12 ΩBIs​4 A

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

V1 = 24 VIs = 4 AR1 = 4 ΩR2 = 6 ΩR3 = 20 ΩR4 = 12 Ω
IR3 = A
4.Medium
R1​ = 15 ΩR3​ = 2 Ω+−V1​9 VR2​5 ΩAR4​3 ΩBIs​2 A

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

V1 = 9 VIs = 2 AR1 = 15 ΩR2 = 5 ΩR3 = 2 ΩR4 = 3 Ω
VB = V
5.Hard
R1​ = 4 ΩIR1​+−Vs​ = 5 V+−V1​15 VR2​2 ΩAR3​4 ΩBIs​4 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 = 15 VIs = 4 AVs = 5 VR1 = 4 ΩR2 = 2 ΩR3 = 4 Ω
IR1 = A
6.Hard
R1​ = 20 ΩR2​ = 5 ΩR4​ = 10 ΩIR4​+−V1​9 VR3​20 ΩAR5​3 ΩBIs​1.5 A+−V2​24 V

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

V1 = 9 VIs = 1.5 AV2 = 24 VR1 = 20 ΩR2 = 5 ΩR3 = 20 ΩR4 = 10 ΩR5 = 3 Ω
IR4 = A

Answer key

  1. 1. IR2 = 2.333 A
  2. 2. IR1 = −0.5469 A
  3. 3. IR3 = −0.9767 A
  4. 4. VB = 4.714 V
  5. 5. IR1 = 1.5 A
  6. 6. IR4 = −2.16 A

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