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​ = 2 Ω+−V1​20 VR2​?AIs​2 A

The node voltage at A is measured as VA = 17 V. Use nodal analysis to find the resistance R2.

V1 = 20 VIs = 2 AR1 = 2 ΩVA = 17 V
R2 = Ω
2.Easy
R1​ = 12 Ω+−V1​8 VR2​?AIs​1 A

The node voltage at A is measured as VA = 4.5 V. Use nodal analysis to find the resistance R2.

V1 = 8 VIs = 1 AR1 = 12 ΩVA = 4.5 V
R2 = Ω
3.Medium
R1​ = 3 ΩR3​ = 2 ΩIR3​+−V1​18 VR2​20 ΩAR4​8 ΩBIs​2.5 A

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

V1 = 18 VIs = 2.5 AR1 = 3 ΩR2 = 20 ΩR3 = 2 ΩR4 = 8 Ω
IR3 = A
4.Medium
R1​ = 4 ΩR3​ = 4 Ω+−V1​6 VR2​4 ΩAR4​3 ΩBIs​5 A

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

V1 = 6 VIs = 5 AR1 = 4 ΩR2 = 4 ΩR3 = 4 ΩR4 = 3 Ω
PIs = W
5.Hard
R1​ = 5 ΩR2​ = 20 ΩR4​ = 8 Ω+−V1​6 VR3​6 ΩAR5​15 ΩBIs​0.5 A+−V2​15 V

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

V1 = 6 VIs = 0.5 AV2 = 15 VR1 = 5 ΩR2 = 20 ΩR3 = 6 ΩR4 = 8 ΩR5 = 15 Ω
VA = V
6.Hard
R1​ = 10 Ω−+Vs​ = 6 V+−V1​24 VR2​5 ΩAR3​30 ΩBIs​5 A

The voltage source Vₛ between A and B has its + terminal at B, so it makes VB − VA = Vₛ. Use nodal analysis with a supernode to find the node voltage VA (measured from ground).

V1 = 24 VIs = 5 AVs = 6 VR1 = 10 ΩR2 = 5 ΩR3 = 30 Ω
VA = V

Answer key

  1. 1. R2 = 4.857 Ω
  2. 2. R2 = 3.484 Ω
  3. 3. IR3 = −0.3448 A
  4. 4. PIs = 55 W
  5. 5. VA = 4.163 V
  6. 6. VA = 21.6 V

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