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​20 VR2​3 ΩAIs​2 A

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

V1 = 20 VIs = 2 AR1 = 6 ΩR2 = 3 Ω
PIs = W
2.Easy
R1​ = 10 ΩR2​ = 8 Ω+−V1​12 VR3​5 ΩIR3​A+−V2​6 V

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

V1 = 12 VV2 = 6 VR1 = 10 ΩR2 = 8 ΩR3 = 5 Ω
IR3 = A
3.Medium
−+Vs​ = 3 VIx​Is​3 AAR1​8 ΩR2​12 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 current Ix through the voltage source, from A to B as shown by the arrow.

Is = 3 AVs = 3 VR1 = 8 ΩR2 = 12 Ω
Ix = A
4.Medium
R1​3 Ω−+V1​6 VR2​3 Ω+−V2​30 VI2​R3​3 Ω+−V3​24 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 = 6 VR1 = 3 ΩV2 = 30 VR2 = 3 ΩV3 = 24 VR3 = 3 Ω
I2 = A
5.Hard
R1​ = 5 ΩIR1​R2​ = 10 ΩR4​ = 4 Ω+−V1​18 VR3​8 ΩAR5​6 ΩBIs​4 A−+V2​6 V

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

V1 = 18 VIs = 4 AV2 = 6 VR1 = 5 ΩR2 = 10 ΩR3 = 8 ΩR4 = 4 ΩR5 = 6 Ω
IR1 = A
6.Hard
R1​ = 6 ΩR2​ = 3 ΩIR2​R4​ = 10 Ω+−V1​24 VR3​2 ΩAR5​12 ΩBIs​0.5 A+−V2​24 V

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

V1 = 24 VIs = 0.5 AV2 = 24 VR1 = 6 ΩR2 = 3 ΩR3 = 2 ΩR4 = 10 ΩR5 = 12 Ω
IR2 = A

Answer key

  1. 1. PIs = 21.33 W
  2. 2. IR3 = 0.9176 A
  3. 3. Ix = 1.35 A
  4. 4. I2 = 4.667 A
  5. 5. IR1 = 2.35 A
  6. 6. IR2 = −0.9863 A

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