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​15 VR2​3 Ω+−V2​8 VR3​3 Ω+−V3​6 VA

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

V1 = 15 VR1 = 8 ΩV2 = 8 VR2 = 3 ΩV3 = 6 VR3 = 3 Ω
VA = V
2.Easy
R1​ = 6 ΩIR1​R2​ = 8 Ω+−V1​24 VR3​2 ΩA+−V2​10 V

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

V1 = 24 VV2 = 10 VR1 = 6 ΩR2 = 8 ΩR3 = 2 Ω
IR1 = A
3.Medium
R1​ = 12 ΩR3​ = 3 Ω+−V1​9 VR2​20 ΩAR4​10 ΩBIs​1.5 A

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

V1 = 9 VIs = 1.5 AR1 = 12 ΩR2 = 20 ΩR3 = 3 ΩR4 = 10 Ω
VA = V
4.Medium
R1​5 Ω+−V1​9 VR2​4 Ω+−V2​12 VR3​8 Ω−+V3​15 VI3​A

Three branches are connected between node A and ground, as shown. Use nodal analysis to find the current I3 in branch 3, flowing up into node A in the direction of the arrow.

V1 = 9 VR1 = 5 ΩV2 = 12 VR2 = 4 ΩV3 = 15 VR3 = 8 Ω
I3 = A
5.Hard
R1​ = 10 ΩR2​ = 3 ΩR4​ = 30 ΩIR4​+−V1​5 VR3​15 ΩAR5​6 ΩBIs​1.5 A−+V2​12 V

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

V1 = 5 VIs = 1.5 AV2 = 12 VR1 = 10 ΩR2 = 3 ΩR3 = 15 ΩR4 = 30 ΩR5 = 6 Ω
IR4 = A
6.Hard
R1​ = 25 ΩIR1​+−Vs​ = 8 V+−V1​15 VR2​5 ΩAR3​4 ΩBIs​1.5 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 IR1 through R1 in the direction of the arrow.

V1 = 15 VIs = 1.5 AVs = 8 VR1 = 25 ΩR2 = 5 ΩR3 = 4 Ω
IR1 = A

Answer key

  1. 1. VA = 8.263 V
  2. 2. IR1 = 2.895 A
  3. 3. VA = 9.055 V
  4. 4. I3 = −2.511 A
  5. 5. IR4 = 0.5536 A
  6. 6. IR1 = 0.2653 A

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