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​ = 10 ΩR2​ = 8 Ω+−V1​15 VR3​5 ΩA+−V2​8 V

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

V1 = 15 VV2 = 8 VR1 = 10 ΩR2 = 8 ΩR3 = 5 Ω
VA = V
2.Easy
R1​ = 12 Ω+−V1​8 VR2​12 ΩAIs​1 A

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

V1 = 8 VIs = 1 AR1 = 12 ΩR2 = 12 Ω
PIs = W
3.Medium
−+Vs​ = 4 VIs​4 AAR1​15 ΩR2​12 ΩB

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).

Is = 4 AVs = 4 VR1 = 15 ΩR2 = 12 Ω
VA = V
4.Medium
R1​ = 6 ΩIR1​R3​ = 12 Ω+−V1​15 VR2​5 ΩAR4​3 ΩBIs​5 A

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

V1 = 15 VIs = 5 AR1 = 6 ΩR2 = 5 ΩR3 = 12 ΩR4 = 3 Ω
IR1 = A
5.Hard
R1​ = 20 ΩR2​ = 12 ΩIR2​R4​ = 30 Ω+−V1​30 VR3​30 ΩAR5​25 ΩBIs​2.5 A+−V2​5 V

Use nodal analysis to find the current IR2 through R2 in the direction of the arrow.

V1 = 30 VIs = 2.5 AV2 = 5 VR1 = 20 ΩR2 = 12 ΩR3 = 30 ΩR4 = 30 ΩR5 = 25 Ω
IR2 = A
6.Hard
R1​ = 10 ΩR2​ = 15 ΩR4​ = 8 ΩIR4​+−V1​18 VR3​20 ΩAR5​15 ΩBIs​1.5 A+−V2​5 V

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

V1 = 18 VIs = 1.5 AV2 = 5 VR1 = 10 ΩR2 = 15 ΩR3 = 20 ΩR4 = 8 ΩR5 = 15 Ω
IR4 = A

Answer key

  1. 1. VA = 5.882 V
  2. 2. PIs = 10 W
  3. 3. VA = 24.44 V
  4. 4. IR1 = 1.154 A
  5. 5. IR2 = −0.4879 A
  6. 6. IR4 = 0.783 A

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