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​ = 12 Ω+−V1​6 VR2​8 ΩAIs​1 A

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

V1 = 6 VIs = 1 AR1 = 12 ΩR2 = 8 Ω
PIs = W
2.Easy
R1​ = 6 Ω+−V1​24 VR2​8 ΩAIs​2 A

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

V1 = 24 VIs = 2 AR1 = 6 ΩR2 = 8 Ω
VA = V
3.Medium
R1​ = 4 ΩR3​ = 8 Ω+−V1​10 VR2​4 ΩAR4​20 ΩBIs​2 A

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

V1 = 10 VIs = 2 AR1 = 4 ΩR2 = 4 ΩR3 = 8 ΩR4 = 20 Ω
VB = V
4.Medium
R1​ = 15 ΩIR1​R3​ = 2 Ω+−V1​6 VR2​5 ΩAR4​20 ΩBIs​1 A

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

V1 = 6 VIs = 1 AR1 = 15 ΩR2 = 5 ΩR3 = 2 ΩR4 = 20 Ω
IR1 = A
5.Hard
R1​ = 20 ΩR2​ = 15 ΩR4​ = 12 ΩIR4​+−V1​18 VR3​10 ΩAR5​6 ΩBIs​5 A+−V2​18 V

Use nodal analysis to find the current IR4 through R4 in the direction of the arrow.

V1 = 18 VIs = 5 AV2 = 18 VR1 = 20 ΩR2 = 15 ΩR3 = 10 ΩR4 = 12 ΩR5 = 6 Ω
IR4 = A
6.Hard
R1​ = 12 ΩR3​ = 20 Ω+−V1​30 VR2​20 ΩAR4​15 ΩBIs​?

The current source is adjusted until the node voltage at A is VA = 19.5 V. Use nodal analysis to find the source current Is (direction as shown).

V1 = 30 VR1 = 12 ΩR2 = 20 ΩR3 = 20 ΩR4 = 15 ΩVA = 19.5 V
Is = A

Answer key

  1. 1. PIs = 7.2 W
  2. 2. VA = 6.857 V
  3. 3. VB = 16.67 V
  4. 4. IR1 = 0.5087 A
  5. 5. IR4 = 0.4069 A
  6. 6. Is = 1.533 A

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