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​18 VR2​5 Ω+−V2​12 VR3​5 ΩA

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

V1 = 18 VR1 = 4 ΩV2 = 12 VR2 = 5 ΩR3 = 5 Ω
VA = V
2.Easy
R1​ = 4 Ω+−V1​24 VR2​6 ΩAIs​1 A

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

V1 = 24 VIs = 1 AR1 = 4 ΩR2 = 6 Ω
VA = V
3.Medium
R1​ = 20 ΩR3​ = 10 Ω+−V1​18 VR2​15 ΩAR4​4 ΩBIs​2 A

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

V1 = 18 VIs = 2 AR1 = 20 ΩR2 = 15 ΩR3 = 10 ΩR4 = 4 Ω
PIs = W
4.Medium
R1​ = 6 ΩR3​ = 5 Ω+−V1​24 VR2​6 ΩAR4​5 ΩBIs​2.5 A

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

V1 = 24 VIs = 2.5 AR1 = 6 ΩR2 = 6 ΩR3 = 5 ΩR4 = 5 Ω
VB = V
5.Hard
R1​ = 4 Ω+−Vs​ = 3 V+−V1​12 VR2​6 ΩAR3​25 ΩBIs​6 A

The voltage source Vₛ between A and B has its + terminal at A, so it makes VA − VB = Vₛ. Use nodal analysis with a supernode to find the node voltage VB (measured from ground).

V1 = 12 VIs = 6 AVs = 3 VR1 = 4 ΩR2 = 6 ΩR3 = 25 Ω
VB = V
6.Hard
R1​ = 6 ΩR3​ = 3 Ω+−V1​12 VR2​2 ΩAR4​8 ΩB0.5·VA​

The diamond is a voltage-controlled current source that pushes a current of 0.5·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 = 6 ΩR2 = 2 ΩR3 = 3 ΩR4 = 8 Ωg = 0.5 A/V
VB = V

Answer key

  1. 1. VA = 10.62 V
  2. 2. VA = 16.8 V
  3. 3. PIs = 15.9 W
  4. 4. VB = 12.31 V
  5. 5. VB = 16.97 V
  6. 6. VB = 9.231 V

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