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​ = 4 Ω+−V1​20 VR3​4 ΩA+−V2​18 V

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

V1 = 20 VV2 = 18 VR1 = 10 ΩR2 = 4 ΩR3 = 4 Ω
VA = V
2.Easy
R1​ = 12 Ω+−V1​12 VR2​10 ΩAIs​2 A

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

V1 = 12 VIs = 2 AR1 = 12 ΩR2 = 10 Ω
PIs = W
3.Medium
R1​ = 5 ΩR3​ = 5 Ω+−V1​18 VR2​2 ΩAR4​8 ΩBIs​4 A

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

V1 = 18 VIs = 4 AR1 = 5 ΩR2 = 2 ΩR3 = 5 ΩR4 = 8 Ω
VB = V
4.Medium
R1​ = 15 ΩR3​ = 3 ΩIR3​+−V1​6 VR2​2 ΩAR4​2 ΩBIs​3 A

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

V1 = 6 VIs = 3 AR1 = 15 ΩR2 = 2 ΩR3 = 3 ΩR4 = 2 Ω
IR3 = A
5.Hard
R1​ = 3 Ω−+Vs​ = 8 VIx​+−V1​24 VR2​30 ΩAR3​6 ΩBIs​2.5 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 current Ix through the voltage source, from A to B as shown by the arrow.

V1 = 24 VIs = 2.5 AVs = 8 VR1 = 3 ΩR2 = 30 ΩR3 = 6 Ω
Ix = A
6.Hard
R1​ = 20 ΩR3​ = 2 Ω+−V1​5 VR2​5 ΩAR4​4 ΩBIs​?

The current source is adjusted until the node voltage at A is VA = 9.5 V. Use nodal analysis to find the source current Is (direction as shown).

V1 = 5 VR1 = 20 ΩR2 = 5 ΩR3 = 2 ΩR4 = 4 ΩVA = 9.5 V
Is = A

Answer key

  1. 1. VA = 10.83 V
  2. 2. PIs = 32.73 W
  3. 3. VB = 17.11 V
  4. 4. IR3 = 0.9913 A
  5. 5. Ix = 1.698 A
  6. 6. Is = 5.563 A

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