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​ = 6 Ω+−V1​24 VR2​3 ΩAIs​1 A

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

V1 = 24 VIs = 1 AR1 = 6 ΩR2 = 3 Ω
PIs = W
2.Easy
R1​ = 3 Ω+−V1​8 VR2​2 ΩIR2​AIs​3 A

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

V1 = 8 VIs = 3 AR1 = 3 ΩR2 = 2 Ω
IR2 = A
3.Medium
R1​ = 6 ΩR3​ = 15 Ω+−V1​9 VR2​20 ΩAR4​8 ΩBIs​3 A

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

V1 = 9 VIs = 3 AR1 = 6 ΩR2 = 20 ΩR3 = 15 ΩR4 = 8 Ω
VB = V
4.Medium
R1​8 Ω+−V1​30 VR2​2 Ω+−V2​10 VI2​R3​4 Ω+−V3​15 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 = 30 VR1 = 8 ΩV2 = 10 VR2 = 2 ΩV3 = 15 VR3 = 4 Ω
I2 = A
5.Hard
R1​ = 4 Ω−+Vs​ = 3 VIx​+−V1​18 VR2​2 ΩAR3​30 ΩBIs​2.5 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 current Ix through the voltage source, from A to B as shown by the arrow.

V1 = 18 VIs = 2.5 AVs = 3 VR1 = 4 ΩR2 = 2 ΩR3 = 30 Ω
Ix = A
6.Hard
R1​ = 12 ΩIR1​R2​ = 6 ΩR4​ = 12 Ω+−V1​6 VR3​20 ΩAR5​15 ΩBIs​2 A+−V2​36 V

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

V1 = 6 VIs = 2 AV2 = 36 VR1 = 12 ΩR2 = 6 ΩR3 = 20 ΩR4 = 12 ΩR5 = 15 Ω
IR1 = A

Answer key

  1. 1. PIs = 10 W
  2. 2. IR2 = −0.2 A
  3. 3. VB = 19.05 V
  4. 4. I2 = −2.143 A
  5. 5. Ix = −2.106 A
  6. 6. IR1 = −0.7293 A

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