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 ΩR2​ = 8 Ω+−V1​20 VR3​2 ΩIR3​A+−V2​20 V

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

V1 = 20 VV2 = 20 VR1 = 4 ΩR2 = 8 ΩR3 = 2 Ω
IR3 = A
2.Easy
R1​2 Ω+−V1​10 VR2​10 Ω+−V2​24 VR3​6 Ω+−V3​12 VA

Three branches are connected between node A and ground, as shown. Use nodal analysis to find the node voltage VA.

V1 = 10 VR1 = 2 ΩV2 = 24 VR2 = 10 ΩV3 = 12 VR3 = 6 Ω
VA = V
3.Medium
R1​2 Ω+−V1​6 VR2​10 Ω+−V2​6 VR3​3 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 = 6 VR1 = 2 ΩV2 = 6 VR2 = 10 ΩR3 = 3 Ω
I3 = A
4.Medium
R1​ = 12 ΩR3​ = 15 Ω+−V1​9 VR2​10 ΩAR4​15 ΩBIs​3 A

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

V1 = 9 VIs = 3 AR1 = 12 ΩR2 = 10 ΩR3 = 15 ΩR4 = 15 Ω
PIs = W
5.Hard
R1​ = 6 ΩR3​ = 30 Ω+−V1​12 VR2​12 ΩAR4​20 ΩBIs​?

The current source is adjusted until the node voltage at A is VA = 16 V. Use nodal analysis to find the source current Is (direction as shown).

V1 = 12 VR1 = 6 ΩR2 = 12 ΩR3 = 30 ΩR4 = 20 ΩVA = 16 V
Is = A
6.Hard
R1​ = 3 ΩIR1​R2​ = 10 ΩR4​ = 10 Ω+−V1​30 VR3​25 ΩAR5​10 ΩBIs​2.5 A−+V2​18 V

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

V1 = 30 VIs = 2.5 AV2 = 18 VR1 = 3 ΩR2 = 10 ΩR3 = 25 ΩR4 = 10 ΩR5 = 10 Ω
IR1 = A

Answer key

  1. 1. IR3 = 4.286 A
  2. 2. VA = 12.26 V
  3. 3. I3 = −1.286 A
  4. 4. PIs = 83.08 W
  5. 5. Is = 5.8 A
  6. 6. IR1 = 2.247 A

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