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​ = 3 Ω+−V1​15 VR2​4 ΩAIs​1 A

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

V1 = 15 VIs = 1 AR1 = 3 ΩR2 = 4 Ω
PIs = W
2.Easy
R1​ = 4 ΩR2​ = 4 ΩIR2​+−V1​10 VR3​5 ΩA+−V2​10 V

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

V1 = 10 VV2 = 10 VR1 = 4 ΩR2 = 4 ΩR3 = 5 Ω
IR2 = A
3.Medium
R1​ = 12 ΩIR1​R3​ = 12 Ω+−V1​9 VR2​3 ΩAR4​4 ΩBIs​4 A

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

V1 = 9 VIs = 4 AR1 = 12 ΩR2 = 3 ΩR3 = 12 ΩR4 = 4 Ω
IR1 = A
4.Medium
R1​ = 12 ΩR3​ = 5 Ω+−V1​24 VR2​2 ΩAR4​20 ΩBIs​4 A

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

V1 = 24 VIs = 4 AR1 = 12 ΩR2 = 2 ΩR3 = 5 ΩR4 = 20 Ω
VA = V
5.Hard
R1​ = 12 Ω+−Vs​ = 9 VIx​+−V1​6 VR2​8 ΩAR3​4 ΩBIs​2 A

The voltage source Vₛ between A and B has its + terminal at A, so it makes VA − VB = Vₛ. Use nodal analysis with a supernode to find the current Ix through the voltage source, from A to B as shown by the arrow.

V1 = 6 VIs = 2 AVs = 9 VR1 = 12 ΩR2 = 8 ΩR3 = 4 Ω
Ix = A
6.Hard
R1​ = 25 ΩR2​ = 6 ΩR4​ = 20 Ω+−V1​24 VR3​8 ΩAR5​4 ΩBIs​0.5 A−+V2​5 V

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

V1 = 24 VIs = 0.5 AV2 = 5 VR1 = 25 ΩR2 = 6 ΩR3 = 8 ΩR4 = 20 ΩR5 = 4 Ω
VB = V

Answer key

  1. 1. PIs = 10.29 W
  2. 2. IR2 = −0.7143 A
  3. 3. IR1 = 0.7935 A
  4. 4. VA = −1.925 V
  5. 5. Ix = −1.659 A
  6. 6. VB = 1.913 V

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