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 ΩIR1​R2​ = 8 Ω+−V1​24 VR3​10 ΩA+−V2​24 V

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

V1 = 24 VV2 = 24 VR1 = 3 ΩR2 = 8 ΩR3 = 10 Ω
IR1 = A
2.Easy
R1​ = 12 Ω+−V1​8 VR2​6 ΩAIs​1 A

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

V1 = 8 VIs = 1 AR1 = 12 ΩR2 = 6 Ω
VA = V
3.Medium
R1​12 Ω+−V1​12 VR2​5 Ω−+V2​15 VR3​10 ΩI3​A

Three branches are connected between node A and ground, as shown. Use nodal analysis to find the current I3 in branch 3, flowing up into node A in the direction of the arrow.

V1 = 12 VR1 = 12 ΩV2 = 15 VR2 = 5 ΩR3 = 10 Ω
I3 = A
4.Medium
R1​ = 20 ΩR3​ = 2 Ω+−V1​15 VR2​5 ΩAR4​20 ΩBIs​5 A

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

V1 = 15 VIs = 5 AR1 = 20 ΩR2 = 5 ΩR3 = 2 ΩR4 = 20 Ω
PIs = W
5.Hard
R1​ = 20 Ω+−Vs​ = 5 V+−V1​15 VR2​20 ΩAR3​5 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 node voltage VA (measured from ground).

V1 = 15 VIs = 6 AVs = 5 VR1 = 20 ΩR2 = 20 ΩR3 = 5 Ω
VA = V
6.Hard
R1​ = 12 ΩR2​ = 10 ΩR4​ = 6 ΩIR4​+−V1​36 VR3​2 ΩAR5​10 ΩBIs​2.5 A+−V2​6 V

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

V1 = 36 VIs = 2.5 AV2 = 6 VR1 = 12 ΩR2 = 10 ΩR3 = 2 ΩR4 = 6 ΩR5 = 10 Ω
IR4 = A

Answer key

  1. 1. IR1 = 1.433 A
  2. 2. VA = −1.333 V
  3. 3. I3 = 0.5217 A
  4. 4. PIs = 126.9 W
  5. 5. VA = 25.83 V
  6. 6. IR4 = 0.8649 A

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