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​ = 4 Ω+−V1​8 VR2​5 ΩAIs​1 A

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

V1 = 8 VIs = 1 AR1 = 4 ΩR2 = 5 Ω
VA = V
2.Easy
R1​ = 3 Ω+−V1​12 VR2​?AIs​2 A

The node voltage at A is measured as VA = 16 V. Use nodal analysis to find the resistance R2.

V1 = 12 VIs = 2 AR1 = 3 ΩVA = 16 V
R2 = Ω
3.Medium
R1​ = 4 ΩR3​ = 3 Ω+−V1​6 VR2​2 ΩAR4​20 ΩBIs​1.5 A

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

V1 = 6 VIs = 1.5 AR1 = 4 ΩR2 = 2 ΩR3 = 3 ΩR4 = 20 Ω
VB = V
4.Medium
R1​ = 3 ΩR3​ = 2 Ω+−V1​15 VR2​6 ΩAR4​3 ΩBIs​1 A

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

V1 = 15 VIs = 1 AR1 = 3 ΩR2 = 6 ΩR3 = 2 ΩR4 = 3 Ω
PIs = W
5.Hard
R1​ = 15 ΩR3​ = 30 Ω+−V1​5 VR2​5 ΩAR4​6 ΩBIs​?

The current source is adjusted until the node voltage at A is VA = 6.5 V. Use nodal analysis to find the source current Is (direction as shown).

V1 = 5 VR1 = 15 ΩR2 = 5 ΩR3 = 30 ΩR4 = 6 ΩVA = 6.5 V
Is = A
6.Hard
R1​ = 30 Ω−+Vs​ = 6 VIx​+−V1​9 VR2​15 ΩAR3​30 ΩBIs​6 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 = 9 VIs = 6 AVs = 6 VR1 = 30 ΩR2 = 15 ΩR3 = 30 Ω
Ix = A

Answer key

  1. 1. VA = 6.667 V
  2. 2. R2 = 24 Ω
  3. 3. VB = 6.986 V
  4. 4. PIs = 6 W
  5. 5. Is = 9.483 A
  6. 6. Ix = −4.275 A

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