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​12 VR2​10 Ω+−V2​24 VR3​6 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 = 12 VR1 = 4 ΩV2 = 24 VR2 = 10 ΩV3 = 6 VR3 = 6 Ω
VA = V
2.Easy
R1​ = 8 ΩR2​ = 10 Ω+−V1​15 VR3​8 ΩA+−V2​10 V

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

V1 = 15 VV2 = 10 VR1 = 8 ΩR2 = 10 ΩR3 = 8 Ω
VA = V
3.Medium
−+Vs​ = 8 VIs​2.5 AAR1​12 ΩR2​6 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 VB (measured from ground).

Is = 2.5 AVs = 8 VR1 = 12 ΩR2 = 6 Ω
VB = V
4.Medium
R1​15 Ω−+V1​30 VR2​6 Ω+−V2​12 VI2​R3​8 Ω+−V3​30 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 = 30 VR1 = 15 ΩV2 = 12 VR2 = 6 ΩV3 = 30 VR3 = 8 Ω
I2 = A
5.Hard
R1​ = 8 ΩIR1​R2​ = 3 ΩR4​ = 5 Ω+−V1​15 VR3​15 ΩAR5​3 ΩBIs​4 A−+V2​6 V

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

V1 = 15 VIs = 4 AV2 = 6 VR1 = 8 ΩR2 = 3 ΩR3 = 15 ΩR4 = 5 ΩR5 = 3 Ω
IR1 = A
6.Hard
R1​ = 25 ΩR2​ = 12 ΩR4​ = 15 ΩIR4​+−V1​36 VR3​10 ΩAR5​15 ΩBIs​3 A−+V2​6 V

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

V1 = 36 VIs = 3 AV2 = 6 VR1 = 25 ΩR2 = 12 ΩR3 = 10 ΩR4 = 15 ΩR5 = 15 Ω
IR4 = A

Answer key

  1. 1. VA = 12.39 V
  2. 2. VA = 8.214 V
  3. 3. VB = 12.67 V
  4. 4. I2 = 0.2558 A
  5. 5. IR1 = 1.914 A
  6. 6. IR4 = 1.527 A

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