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 ΩR2​ = 2 Ω+−V1​8 VR3​3 ΩIR3​A+−V2​8 V

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

V1 = 8 VV2 = 8 VR1 = 12 ΩR2 = 2 ΩR3 = 3 Ω
IR3 = A
2.Easy
R1​ = 12 Ω+−V1​6 VR2​?AIs​3 A

The node voltage at A is measured as VA = 34.5 V. Use nodal analysis to find the resistance R2.

V1 = 6 VIs = 3 AR1 = 12 ΩVA = 34.5 V
R2 = Ω
3.Medium
R1​ = 8 ΩR3​ = 3 Ω+−V1​18 VR2​12 ΩAR4​6 ΩBIs​3 A

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

V1 = 18 VIs = 3 AR1 = 8 ΩR2 = 12 ΩR3 = 3 ΩR4 = 6 Ω
VA = V
4.Medium
R1​ = 10 ΩR3​ = 20 Ω+−V1​10 VR2​20 ΩAR4​5 ΩBIs​1.5 A

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

V1 = 10 VIs = 1.5 AR1 = 10 ΩR2 = 20 ΩR3 = 20 ΩR4 = 5 Ω
PIs = W
5.Hard
R1​ = 10 ΩR3​ = 30 Ω+−V1​9 VR2​12 ΩAR4​30 ΩBIs​?

The current source is adjusted until the node voltage at A is VA = 10 V. Use nodal analysis to find the source current Is (direction as shown).

V1 = 9 VR1 = 10 ΩR2 = 12 ΩR3 = 30 ΩR4 = 30 ΩVA = 10 V
Is = A
6.Hard
R1​ = 3 ΩR2​ = 4 ΩR4​ = 25 ΩIR4​+−V1​12 VR3​2 ΩAR5​20 ΩBIs​3 A+−V2​6 V

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

V1 = 12 VIs = 3 AV2 = 6 VR1 = 3 ΩR2 = 4 ΩR3 = 2 ΩR4 = 25 ΩR5 = 20 Ω
IR4 = A

Answer key

  1. 1. IR3 = 1.697 A
  2. 2. R2 = 55.2 Ω
  3. 3. VA = 13.3 V
  4. 4. PIs = 11.05 W
  5. 5. Is = 2.2 A
  6. 6. IR4 = 0.3499 A

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