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​3 A

Use nodal analysis to find the power PIs delivered by the current source Is.

V1 = 20 VIs = 3 AR1 = 4 ΩR2 = 3 Ω
PIs = W
2.Easy
R1​8 Ω+−V1​6 VR2​2 Ω+−V2​15 VR3​6 Ω+−V3​12 VA

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

V1 = 6 VR1 = 8 ΩV2 = 15 VR2 = 2 ΩV3 = 12 VR3 = 6 Ω
VA = V
3.Medium
R1​ = 8 ΩR3​ = 8 Ω+−V1​6 VR2​8 ΩAR4​6 ΩBIs​2 A

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

V1 = 6 VIs = 2 AR1 = 8 ΩR2 = 8 ΩR3 = 8 ΩR4 = 6 Ω
VA = V
4.Medium
−+Vs​ = 12 VIs​5 AAR1​6 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 = 5 AVs = 12 VR1 = 6 ΩR2 = 4 Ω
VA = V
5.Hard
R1​ = 25 ΩR3​ = 5 Ω+−V1​24 VR2​10 ΩAR4​25 ΩBIs​?

The current source is adjusted until the node voltage at A is VA = 9.5 V. Use nodal analysis to find the source current Is (direction as shown).

V1 = 24 VR1 = 25 ΩR2 = 10 ΩR3 = 5 ΩR4 = 25 ΩVA = 9.5 V
Is = A
6.Hard
R1​ = 2 ΩR3​ = 3 Ω+−V1​12 VR2​25 ΩAR4​20 ΩB0.05·VA​

The diamond is a voltage-controlled current source that pushes a current of 0.05·VA (in A, with VA in V) up into node B. Use nodal analysis to find the node voltage VB (measured from ground).

V1 = 12 VR1 = 2 ΩR2 = 25 ΩR3 = 3 ΩR4 = 20 Ωg = 0.05 A/V
VB = V

Answer key

  1. 1. PIs = 41.14 W
  2. 2. VA = 12.95 V
  3. 3. VA = 5 V
  4. 4. VA = 4.8 V
  5. 5. Is = 0.824 A
  6. 6. VB = 11.11 V

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