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​10 VR2​12 Ω+−V2​10 VR3​5 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 = 5 ΩV2 = 10 VR2 = 12 ΩV3 = 12 VR3 = 5 Ω
VA = V
2.Easy
R1​ = 2 Ω+−V1​20 VR2​6 ΩAIs​2 A

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

V1 = 20 VIs = 2 AR1 = 2 ΩR2 = 6 Ω
PIs = W
3.Medium
R1​ = 20 ΩR3​ = 8 Ω+−V1​30 VR2​8 ΩAR4​4 ΩBIs​2.5 A

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

V1 = 30 VIs = 2.5 AR1 = 20 ΩR2 = 8 ΩR3 = 8 ΩR4 = 4 Ω
VB = V
4.Medium
R1​8 Ω−+V1​18 VI1​R2​3 Ω+−V2​9 VR3​6 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 = 18 VR1 = 8 ΩV2 = 9 VR2 = 3 ΩV3 = 12 VR3 = 6 Ω
I1 = A
5.Hard
R1​ = 30 ΩR3​ = 5 Ω+−V1​10 VR2​4 ΩAR4​20 ΩBIs​?

The current source is adjusted until the node voltage at A is VA = 15.5 V. Use nodal analysis to find the source current Is (direction as shown).

V1 = 10 VR1 = 30 ΩR2 = 4 ΩR3 = 5 ΩR4 = 20 ΩVA = 15.5 V
Is = A
6.Hard
R1​ = 25 ΩR2​ = 6 ΩR4​ = 25 Ω+−V1​10 VR3​5 ΩAR5​3 ΩBIs​1.5 A+−V2​18 V

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

V1 = 10 VIs = 1.5 AV2 = 18 VR1 = 25 ΩR2 = 6 ΩR3 = 5 ΩR4 = 25 ΩR5 = 3 Ω
VA = V

Answer key

  1. 1. VA = 10.83 V
  2. 2. PIs = 36 W
  3. 3. VB = 9.677 V
  4. 4. I1 = −2.8 A
  5. 5. Is = 5.848 A
  6. 6. VA = 0.4483 V

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