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​ = 4 Ω+−V1​12 VR2​12 ΩAIs​2 A

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

V1 = 12 VIs = 2 AR1 = 4 ΩR2 = 12 Ω
PIs = W
2.Easy
R1​ = 8 Ω+−V1​20 VR2​2 ΩIR2​AIs​2 A

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

V1 = 20 VIs = 2 AR1 = 8 ΩR2 = 2 Ω
IR2 = A
3.Medium
R1​ = 12 ΩR3​ = 2 Ω+−V1​24 VR2​4 ΩAR4​5 ΩBIs​2.5 A

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

V1 = 24 VIs = 2.5 AR1 = 12 ΩR2 = 4 ΩR3 = 2 ΩR4 = 5 Ω
VB = V
4.Medium
R1​5 Ω+−V1​24 VR2​4 Ω+−V2​30 VR3​4 Ω+−V3​24 VI3​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 = 24 VR1 = 5 ΩV2 = 30 VR2 = 4 ΩV3 = 24 VR3 = 4 Ω
I3 = A
5.Hard
R1​ = 25 Ω−+Vs​ = 4 V+−V1​30 VR2​2 ΩAR3​8 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 node voltage VB (measured from ground).

V1 = 30 VIs = 2 AVs = 4 VR1 = 25 ΩR2 = 2 ΩR3 = 8 Ω
VB = V
6.Hard
R1​ = 20 ΩR2​ = 12 ΩR4​ = 12 Ω+−V1​10 VR3​10 ΩAR5​6 ΩBIs​1.5 A+−V2​36 V

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

V1 = 10 VIs = 1.5 AV2 = 36 VR1 = 20 ΩR2 = 12 ΩR3 = 10 ΩR4 = 12 ΩR5 = 6 Ω
VA = V

Answer key

  1. 1. PIs = 30 W
  2. 2. IR2 = 3.6 A
  3. 3. VB = 9.25 V
  4. 4. I3 = −0.5357 A
  5. 5. VB = 8.06 V
  6. 6. VA = 4.118 V

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