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​ = 3 Ω+−V1​24 VR2​4 ΩIR2​AIs​1 A

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

V1 = 24 VIs = 1 AR1 = 3 ΩR2 = 4 Ω
IR2 = A
2.Easy
R1​ = 8 ΩR2​ = 10 Ω+−V1​6 VR3​8 ΩIR3​A+−V2​20 V

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

V1 = 6 VV2 = 20 VR1 = 8 ΩR2 = 10 ΩR3 = 8 Ω
IR3 = A
3.Medium
R1​ = 3 ΩR3​ = 3 Ω+−V1​12 VR2​15 ΩAR4​10 ΩBIs​1 A

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

V1 = 12 VIs = 1 AR1 = 3 ΩR2 = 15 ΩR3 = 3 ΩR4 = 10 Ω
PIs = W
4.Medium
−+Vs​ = 4 VIs​3 AAR1​8 ΩR2​5 ΩB

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).

Is = 3 AVs = 4 VR1 = 8 ΩR2 = 5 Ω
VB = V
5.Hard
R1​ = 8 ΩIR1​R2​ = 30 ΩR4​ = 5 Ω+−V1​30 VR3​2 ΩAR5​25 ΩBIs​2.5 A−+V2​30 V

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

V1 = 30 VIs = 2.5 AV2 = 30 VR1 = 8 ΩR2 = 30 ΩR3 = 2 ΩR4 = 5 ΩR5 = 25 Ω
IR1 = A
6.Hard
R1​ = 12 ΩR3​ = 20 Ω+−V1​9 VR2​5 ΩAR4​20 ΩB0.05·VA​

The diamond is a voltage-controlled current source that pushes a current of 0.05·VA (in A, with VA in V) up into node B. Use nodal analysis to find the node voltage VA (measured from ground).

V1 = 9 VR1 = 12 ΩR2 = 5 ΩR3 = 20 ΩR4 = 20 Ωg = 0.05 A/V
VA = V

Answer key

  1. 1. IR2 = 3.857 A
  2. 2. IR3 = 0.9821 A
  3. 3. PIs = 10 W
  4. 4. VB = 10.77 V
  5. 5. IR1 = 3.115 A
  6. 6. VA = 2.647 V

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