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​ = 5 Ω+−V1​24 VR2​3 ΩAIs​2 A

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

V1 = 24 VIs = 2 AR1 = 5 ΩR2 = 3 Ω
PIs = W
2.Easy
R1​ = 2 ΩR2​ = 5 ΩIR2​+−V1​12 VR3​5 ΩA+−V2​20 V

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

V1 = 12 VV2 = 20 VR1 = 2 ΩR2 = 5 ΩR3 = 5 Ω
IR2 = A
3.Medium
R1​ = 12 ΩR3​ = 5 ΩIR3​+−V1​24 VR2​8 ΩAR4​6 ΩBIs​4 A

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

V1 = 24 VIs = 4 AR1 = 12 ΩR2 = 8 ΩR3 = 5 ΩR4 = 6 Ω
IR3 = A
4.Medium
R1​10 Ω+−V1​15 VI1​R2​15 Ω+−V2​15 VR3​10 Ω+−V3​12 VA

Three branches are connected between node A and ground, as shown. Use nodal analysis to find the current I1 in branch 1, flowing up into node A in the direction of the arrow.

V1 = 15 VR1 = 10 ΩV2 = 15 VR2 = 15 ΩV3 = 12 VR3 = 10 Ω
I1 = A
5.Hard
R1​ = 2 ΩR2​ = 3 ΩR4​ = 12 Ω+−V1​6 VR3​10 ΩAR5​3 ΩBIs​2.5 A+−V2​24 V

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

V1 = 6 VIs = 2.5 AV2 = 24 VR1 = 2 ΩR2 = 3 ΩR3 = 10 ΩR4 = 12 ΩR5 = 3 Ω
VB = V
6.Hard
R1​ = 20 ΩR3​ = 6 Ω+−V1​24 VR2​10 ΩAR4​8 ΩBIs​?

The current source is adjusted until the node voltage at A is VA = 18 V. Use nodal analysis to find the source current Is (direction as shown).

V1 = 24 VR1 = 20 ΩR2 = 10 ΩR3 = 6 ΩR4 = 8 ΩVA = 18 V
Is = A

Answer key

  1. 1. PIs = 25.5 W
  2. 2. IR2 = −1.778 A
  3. 3. IR3 = 2.127 A
  4. 4. I1 = 0.1125 A
  5. 5. VB = 8.83 V
  6. 6. Is = 4.875 A

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