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​6 VR2​8 ΩIR2​AIs​1 A

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

V1 = 6 VIs = 1 AR1 = 3 ΩR2 = 8 Ω
IR2 = A
2.Easy
R1​ = 4 Ω+−V1​10 VR2​2 ΩAIs​2 A

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

V1 = 10 VIs = 2 AR1 = 4 ΩR2 = 2 Ω
PIs = W
3.Medium
R1​ = 6 ΩR3​ = 5 ΩIR3​+−V1​12 VR2​15 ΩAR4​4 ΩBIs​2.5 A

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

V1 = 12 VIs = 2.5 AR1 = 6 ΩR2 = 15 ΩR3 = 5 ΩR4 = 4 Ω
IR3 = A
4.Medium
R1​5 Ω+−V1​9 VR2​5 Ω+−V2​9 VI2​R3​3 Ω+−V3​10 VA

Three branches are connected between node A and ground, as shown. Use nodal analysis to find the current I2 in branch 2, flowing up into node A in the direction of the arrow.

V1 = 9 VR1 = 5 ΩV2 = 9 VR2 = 5 ΩV3 = 10 VR3 = 3 Ω
I2 = A
5.Hard
R1​ = 12 ΩR2​ = 20 ΩR4​ = 15 ΩIR4​+−V1​12 VR3​10 ΩAR5​12 ΩBIs​2.5 A−+V2​12 V

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

V1 = 12 VIs = 2.5 AV2 = 12 VR1 = 12 ΩR2 = 20 ΩR3 = 10 ΩR4 = 15 ΩR5 = 12 Ω
IR4 = A
6.Hard
R1​ = 6 Ω−+Vs​ = 5 V+−V1​18 VR2​30 ΩAR3​6 ΩBIs​1.5 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 = 18 VIs = 1.5 AVs = 5 VR1 = 6 ΩR2 = 30 ΩR3 = 6 Ω
VB = V

Answer key

  1. 1. IR2 = 0.8182 A
  2. 2. PIs = 12 W
  3. 3. IR3 = −0.1075 A
  4. 4. I2 = −0.09091 A
  5. 5. IR4 = −0.2868 A
  6. 6. VB = 15 V

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