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​5 Ω+−V1​18 VR2​3 Ω+−V2​8 VR3​5 Ω+−V3​18 VA

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

V1 = 18 VR1 = 5 ΩV2 = 8 VR2 = 3 ΩV3 = 18 VR3 = 5 Ω
VA = V
2.Easy
R1​ = 10 Ω+−V1​18 VR2​6 ΩIR2​AIs​3 A

Use nodal analysis to find the current IR2 through R2 in the direction of the arrow.

V1 = 18 VIs = 3 AR1 = 10 ΩR2 = 6 Ω
IR2 = A
3.Medium
R1​ = 12 ΩR3​ = 20 Ω+−V1​6 VR2​2 ΩAR4​20 ΩBIs​2 A

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

V1 = 6 VIs = 2 AR1 = 12 ΩR2 = 2 ΩR3 = 20 ΩR4 = 20 Ω
VB = V
4.Medium
−+Vs​ = 8 VIs​5 AAR1​6 ΩR2​15 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 = 5 AVs = 8 VR1 = 6 ΩR2 = 15 Ω
VA = V
5.Hard
R1​ = 12 ΩR3​ = 8 Ω+−V1​12 VR2​6 ΩAR4​6 ΩBIs​?

The current source is adjusted until the node voltage at A is VA = 14 V. Use nodal analysis to find the source current Is (direction as shown).

V1 = 12 VR1 = 12 ΩR2 = 6 ΩR3 = 8 ΩR4 = 6 ΩVA = 14 V
Is = A
6.Hard
R1​ = 10 ΩIR1​R2​ = 10 ΩR4​ = 12 Ω+−V1​18 VR3​4 ΩAR5​30 ΩBIs​3 A+−V2​10 V

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

V1 = 18 VIs = 3 AV2 = 10 VR1 = 10 ΩR2 = 10 ΩR3 = 4 ΩR4 = 12 ΩR5 = 30 Ω
IR1 = A

Answer key

  1. 1. VA = 13.45 V
  2. 2. IR2 = 3 A
  3. 3. VB = 21.23 V
  4. 4. VA = 19.14 V
  5. 5. Is = 8.167 A
  6. 6. IR1 = 0.9162 A

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