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​ = 8 Ω+−V1​10 VR2​3 ΩAIs​2 A

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

V1 = 10 VIs = 2 AR1 = 8 ΩR2 = 3 Ω
VA = V
2.Easy
R1​ = 6 Ω+−V1​6 VR2​10 ΩAIs​3 A

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

V1 = 6 VIs = 3 AR1 = 6 ΩR2 = 10 Ω
PIs = W
3.Medium
R1​ = 15 ΩR3​ = 8 Ω+−V1​18 VR2​15 ΩAR4​10 ΩBIs​4 A

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

V1 = 18 VIs = 4 AR1 = 15 ΩR2 = 15 ΩR3 = 8 ΩR4 = 10 Ω
VB = V
4.Medium
R1​12 Ω+−V1​18 VI1​R2​5 Ω−+V2​9 VR3​4 Ω+−V3​9 VA

Three branches are connected between node A and ground, as shown. Use nodal analysis to find the current I1 in branch 1, flowing up into node A in the direction of the arrow.

V1 = 18 VR1 = 12 ΩV2 = 9 VR2 = 5 ΩV3 = 9 VR3 = 4 Ω
I1 = A
5.Hard
R1​ = 8 ΩIR1​R2​ = 8 ΩR4​ = 8 Ω+−V1​30 VR3​8 ΩAR5​3 ΩBIs​1 A+−V2​6 V

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

V1 = 30 VIs = 1 AV2 = 6 VR1 = 8 ΩR2 = 8 ΩR3 = 8 ΩR4 = 8 ΩR5 = 3 Ω
IR1 = A
6.Hard
R1​ = 4 Ω+−Vs​ = 5 VIx​+−V1​15 VR2​20 ΩAR3​3 ΩBIs​1 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 = 15 VIs = 1 AVs = 5 VR1 = 4 ΩR2 = 20 ΩR3 = 3 Ω
Ix = A

Answer key

  1. 1. VA = 7.091 V
  2. 2. PIs = 45 W
  3. 3. VB = 27.84 V
  4. 4. I1 = 1.195 A
  5. 5. IR1 = 2.269 A
  6. 6. Ix = 0.7105 A

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