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​12 ΩAIs​3 A

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

V1 = 18 VIs = 3 AR1 = 8 ΩR2 = 12 Ω
PIs = W
2.Easy
R1​ = 6 Ω+−V1​15 VR2​8 ΩIR2​AIs​2 A

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

V1 = 15 VIs = 2 AR1 = 6 ΩR2 = 8 Ω
IR2 = A
3.Medium
R1​ = 20 ΩIR1​R3​ = 10 Ω+−V1​12 VR2​6 ΩAR4​8 ΩBIs​1 A

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

V1 = 12 VIs = 1 AR1 = 20 ΩR2 = 6 ΩR3 = 10 ΩR4 = 8 Ω
IR1 = A
4.Medium
R1​ = 2 ΩR3​ = 6 Ω+−V1​9 VR2​3 ΩAR4​3 ΩBIs​3 A

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

V1 = 9 VIs = 3 AR1 = 2 ΩR2 = 3 ΩR3 = 6 ΩR4 = 3 Ω
VA = V
5.Hard
R1​ = 15 ΩIR1​−+Vs​ = 15 V+−V1​30 VR2​4 ΩAR3​2 ΩBIs​2 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 = 30 VIs = 2 AVs = 15 VR1 = 15 ΩR2 = 4 ΩR3 = 2 Ω
IR1 = A
6.Hard
R1​ = 12 Ω+−Vs​ = 3 V+−V1​9 VR2​4 ΩAR3​2 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 node voltage VA (measured from ground).

V1 = 9 VIs = 1 AVs = 3 VR1 = 12 ΩR2 = 4 ΩR3 = 2 Ω
VA = V

Answer key

  1. 1. PIs = 75.6 W
  2. 2. IR2 = 0.2143 A
  3. 3. IR1 = 0.4082 A
  4. 4. VA = 5.824 V
  5. 5. IR1 = 2.286 A
  6. 6. VA = 3.9 V

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