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​24 VR2​2 Ω+−V2​8 VR3​4 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 = 24 VR1 = 4 ΩV2 = 8 VR2 = 2 ΩV3 = 6 VR3 = 4 Ω
VA = V
2.Easy
R1​ = 10 Ω+−V1​12 VR2​?AIs​1 A

The node voltage at A is measured as VA = 19.5 V. Use nodal analysis to find the resistance R2.

V1 = 12 VIs = 1 AR1 = 10 ΩVA = 19.5 V
R2 = Ω
3.Medium
R1​ = 8 ΩIR1​R3​ = 6 Ω+−V1​12 VR2​8 ΩAR4​12 ΩBIs​1.5 A

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

V1 = 12 VIs = 1.5 AR1 = 8 ΩR2 = 8 ΩR3 = 6 ΩR4 = 12 Ω
IR1 = A
4.Medium
−+Vs​ = 3 VIs​2.5 AAR1​3 ΩR2​4 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 VA (measured from ground).

Is = 2.5 AVs = 3 VR1 = 3 ΩR2 = 4 Ω
VA = V
5.Hard
R1​ = 5 ΩR3​ = 8 Ω+−V1​10 VR2​8 ΩAR4​20 ΩBIs​?

The current source is adjusted until the node voltage at A is VA = 6 V. Use nodal analysis to find the source current Is (direction as shown).

V1 = 10 VR1 = 5 ΩR2 = 8 ΩR3 = 8 ΩR4 = 20 ΩVA = 6 V
Is = A
6.Hard
R1​ = 25 ΩR2​ = 2 ΩR4​ = 3 Ω+−V1​10 VR3​10 ΩAR5​3 ΩBIs​2.5 A+−V2​10 V

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

V1 = 10 VIs = 2.5 AV2 = 10 VR1 = 25 ΩR2 = 2 ΩR3 = 10 ΩR4 = 3 ΩR5 = 3 Ω
VA = V

Answer key

  1. 1. VA = 11.5 V
  2. 2. R2 = 78 Ω
  3. 3. IR1 = 0.4773 A
  4. 4. VA = 3 V
  5. 5. Is = 0.23 A
  6. 6. VA = 6.812 V

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