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​2 Ω+−V1​8 VR2​8 Ω+−V2​15 VR3​2 ΩA

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

V1 = 8 VR1 = 2 ΩV2 = 15 VR2 = 8 ΩR3 = 2 Ω
VA = V
2.Easy
R1​ = 12 ΩR2​ = 10 Ω+−V1​10 VR3​12 ΩA+−V2​15 V

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

V1 = 10 VV2 = 15 VR1 = 12 ΩR2 = 10 ΩR3 = 12 Ω
VA = V
3.Medium
−+Vs​ = 5 VIx​Is​1.5 AAR1​12 ΩR2​10 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 current Ix through the voltage source, from A to B as shown by the arrow.

Is = 1.5 AVs = 5 VR1 = 12 ΩR2 = 10 Ω
Ix = A
4.Medium
R1​ = 10 ΩR3​ = 15 Ω+−V1​6 VR2​6 ΩAR4​4 ΩBIs​4 A

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

V1 = 6 VIs = 4 AR1 = 10 ΩR2 = 6 ΩR3 = 15 ΩR4 = 4 Ω
VB = V
5.Hard
R1​ = 25 ΩR3​ = 8 Ω+−V1​12 VR2​12 ΩAR4​3 ΩBIs​?

The current source is adjusted until the node voltage at A is VA = 13.5 V. Use nodal analysis to find the source current Is (direction as shown).

V1 = 12 VR1 = 25 ΩR2 = 12 ΩR3 = 8 ΩR4 = 3 ΩVA = 13.5 V
Is = A
6.Hard
R1​ = 2 ΩIR1​−+Vs​ = 4 V+−V1​30 VR2​12 ΩAR3​2 ΩBIs​0.5 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 current IR1 through R1 in the direction of the arrow.

V1 = 30 VIs = 0.5 AVs = 4 VR1 = 2 ΩR2 = 12 ΩR3 = 2 Ω
IR1 = A

Answer key

  1. 1. VA = 5.222 V
  2. 2. VA = 8.75 V
  3. 3. Ix = 1.045 A
  4. 4. VB = 13.58 V
  5. 5. Is = 8.845 A
  6. 6. IR1 = 8.769 A

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