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 ΩIR1​R2​ = 3 Ω+−V1​15 VR3​5 ΩA+−V2​6 V

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

V1 = 15 VV2 = 6 VR1 = 6 ΩR2 = 3 ΩR3 = 5 Ω
IR1 = A
2.Easy
R1​ = 2 Ω+−V1​12 VR2​5 ΩAIs​1 A

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

V1 = 12 VIs = 1 AR1 = 2 ΩR2 = 5 Ω
PIs = W
3.Medium
R1​ = 10 ΩR3​ = 4 Ω+−V1​12 VR2​5 ΩAR4​12 ΩBIs​1 A

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

V1 = 12 VIs = 1 AR1 = 10 ΩR2 = 5 ΩR3 = 4 ΩR4 = 12 Ω
VA = V
4.Medium
R1​6 Ω+−V1​30 VR2​8 Ω−+V2​6 VR3​5 Ω+−V3​6 VI3​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 = 30 VR1 = 6 ΩV2 = 6 VR2 = 8 ΩV3 = 6 VR3 = 5 Ω
I3 = A
5.Hard
R1​ = 4 ΩR2​ = 10 ΩR4​ = 3 Ω+−V1​30 VR3​4 ΩAR5​3 ΩBIs​1.5 A+−V2​9 V

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

V1 = 30 VIs = 1.5 AV2 = 9 VR1 = 4 ΩR2 = 10 ΩR3 = 4 ΩR4 = 3 ΩR5 = 3 Ω
VB = V
6.Hard
R1​ = 5 ΩR3​ = 2 Ω+−V1​30 VR2​5 ΩAR4​20 ΩBIs​?

The current source is adjusted until the node voltage at A is VA = 24 V. Use nodal analysis to find the source current Is (direction as shown).

V1 = 30 VR1 = 5 ΩR2 = 5 ΩR3 = 2 ΩR4 = 20 ΩVA = 24 V
Is = A

Answer key

  1. 1. IR1 = 1.429 A
  2. 2. PIs = 10 W
  3. 3. VA = 5.379 V
  4. 4. I3 = −1.017 A
  5. 5. VB = 7.667 V
  6. 6. Is = 5.16 A

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