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​20 VR2​3 ΩAIs​2 A

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

V1 = 20 VIs = 2 AR1 = 4 ΩR2 = 3 Ω
VA = V
2.Easy
R1​ = 12 ΩIR1​+−V1​6 VR2​6 ΩAIs​3 A

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

V1 = 6 VIs = 3 AR1 = 12 ΩR2 = 6 Ω
IR1 = A
3.Medium
R1​6 Ω+−V1​15 VR2​12 Ω+−V2​9 VI2​R3​6 Ω+−V3​9 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 = 15 VR1 = 6 ΩV2 = 9 VR2 = 12 ΩV3 = 9 VR3 = 6 Ω
I2 = A
4.Medium
R1​ = 4 ΩR3​ = 20 Ω+−V1​12 VR2​3 ΩAR4​8 ΩBIs​5 A

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

V1 = 12 VIs = 5 AR1 = 4 ΩR2 = 3 ΩR3 = 20 ΩR4 = 8 Ω
VB = V
5.Hard
R1​ = 15 Ω−+Vs​ = 12 V+−V1​10 VR2​2 ΩAR3​4 ΩBIs​5 A

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).

V1 = 10 VIs = 5 AVs = 12 VR1 = 15 ΩR2 = 2 ΩR3 = 4 Ω
VA = V
6.Hard
R1​ = 6 ΩR3​ = 30 Ω+−V1​9 VR2​25 ΩAR4​8 ΩBIs​?

The current source is adjusted until the node voltage at A is VA = 7.5 V. Use nodal analysis to find the source current Is (direction as shown).

V1 = 9 VR1 = 6 ΩR2 = 25 ΩR3 = 30 ΩR4 = 8 ΩVA = 7.5 V
Is = A

Answer key

  1. 1. VA = 12 V
  2. 2. IR1 = −0.6667 A
  3. 3. I2 = −0.2 A
  4. 4. VB = 30.62 V
  5. 5. VA = 3.265 V
  6. 6. Is = 1.175 A

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