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​ = 2 Ω+−V1​10 VR3​2 ΩA+−V2​18 V

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

V1 = 10 VV2 = 18 VR1 = 10 ΩR2 = 2 ΩR3 = 2 Ω
VA = V
2.Easy
R1​2 Ω+−V1​18 VR2​8 Ω+−V2​18 VR3​2 Ω+−V3​15 VA

Three branches are connected between node A and ground, as shown. Use nodal analysis to find the node voltage VA.

V1 = 18 VR1 = 2 ΩV2 = 18 VR2 = 8 ΩV3 = 15 VR3 = 2 Ω
VA = V
3.Medium
R1​10 Ω+−V1​24 VR2​2 Ω+−V2​24 VI2​R3​15 Ω+−V3​12 VA

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 = 24 VR1 = 10 ΩV2 = 24 VR2 = 2 ΩV3 = 12 VR3 = 15 Ω
I2 = A
4.Medium
R1​ = 5 ΩR3​ = 20 Ω+−V1​18 VR2​20 ΩAR4​5 ΩBIs​1 A

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

V1 = 18 VIs = 1 AR1 = 5 ΩR2 = 20 ΩR3 = 20 ΩR4 = 5 Ω
VB = V
5.Hard
R1​ = 6 ΩR2​ = 2 ΩR4​ = 3 ΩIR4​+−V1​24 VR3​30 ΩAR5​15 ΩBIs​5 A−+V2​12 V

Use nodal analysis to find the current IR4 through R4 in the direction of the arrow.

V1 = 24 VIs = 5 AV2 = 12 VR1 = 6 ΩR2 = 2 ΩR3 = 30 ΩR4 = 3 ΩR5 = 15 Ω
IR4 = A
6.Hard
R1​ = 20 Ω+−Vs​ = 5 V+−V1​18 VR2​3 ΩAR3​20 ΩBIs​4 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 node voltage VB (measured from ground).

V1 = 18 VIs = 4 AVs = 5 VR1 = 20 ΩR2 = 3 ΩR3 = 20 Ω
VB = V

Answer key

  1. 1. VA = 9.091 V
  2. 2. VA = 16.67 V
  3. 3. I2 = 0.6 A
  4. 4. VB = 6.621 V
  5. 5. IR4 = 6.368 A
  6. 6. VB = 6.885 V

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