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​ = 6 ΩR2​ = 10 Ω+−V1​15 VR3​4 ΩA+−V2​8 V

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

V1 = 15 VV2 = 8 VR1 = 6 ΩR2 = 10 ΩR3 = 4 Ω
VA = V
2.Easy
R1​ = 10 Ω+−V1​20 VR2​6 ΩAIs​3 A

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

V1 = 20 VIs = 3 AR1 = 10 ΩR2 = 6 Ω
PIs = W
3.Medium
−+Vs​ = 5 VIs​1.5 AAR1​2 ΩR2​2 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 = 1.5 AVs = 5 VR1 = 2 ΩR2 = 2 Ω
VA = V
4.Medium
R1​8 Ω+−V1​15 VR2​2 Ω+−V2​6 VI2​R3​2 ΩA

Three branches are connected between node A and ground, as shown. Use nodal analysis to find the current I2 in branch 2, flowing up into node A in the direction of the arrow.

V1 = 15 VR1 = 8 ΩV2 = 6 VR2 = 2 ΩR3 = 2 Ω
I2 = A
5.Hard
R1​ = 12 ΩR2​ = 3 ΩIR2​R4​ = 8 Ω+−V1​30 VR3​12 ΩAR5​6 ΩBIs​0.5 A−+V2​9 V

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

V1 = 30 VIs = 0.5 AV2 = 9 VR1 = 12 ΩR2 = 3 ΩR3 = 12 ΩR4 = 8 ΩR5 = 6 Ω
IR2 = A
6.Hard
R1​ = 10 ΩR2​ = 30 ΩR4​ = 2 Ω+−V1​5 VR3​15 ΩAR5​8 ΩBIs​1.5 A−+V2​12 V

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

V1 = 5 VIs = 1.5 AV2 = 12 VR1 = 10 ΩR2 = 30 ΩR3 = 15 ΩR4 = 2 ΩR5 = 8 Ω
VB = V

Answer key

  1. 1. VA = 6.387 V
  2. 2. PIs = 56.25 W
  3. 3. VA = −1 V
  4. 4. I2 = 0.8333 A
  5. 5. IR2 = 1.379 A
  6. 6. VB = −6.766 V

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