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​3 Ω+−V1​10 VR2​8 Ω+−V2​12 VR3​4 ΩA

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

V1 = 10 VR1 = 3 ΩV2 = 12 VR2 = 8 ΩR3 = 4 Ω
VA = V
2.Easy
R1​ = 6 Ω+−V1​8 VR2​3 ΩAIs​2 A

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

V1 = 8 VIs = 2 AR1 = 6 ΩR2 = 3 Ω
PIs = W
3.Medium
R1​10 Ω+−V1​15 VR2​12 Ω+−V2​24 VR3​10 Ω+−V3​18 VI3​A

Three branches are connected between node A and ground, as shown. Use nodal analysis to find the current I3 in branch 3, flowing up into node A in the direction of the arrow.

V1 = 15 VR1 = 10 ΩV2 = 24 VR2 = 12 ΩV3 = 18 VR3 = 10 Ω
I3 = A
4.Medium
R1​ = 5 ΩR3​ = 12 Ω+−V1​24 VR2​8 ΩAR4​5 ΩBIs​4 A

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

V1 = 24 VIs = 4 AR1 = 5 ΩR2 = 8 ΩR3 = 12 ΩR4 = 5 Ω
VA = V
5.Hard
R1​ = 4 Ω−+Vs​ = 5 V+−V1​10 VR2​6 ΩAR3​25 ΩBIs​1 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 node voltage VB (measured from ground).

V1 = 10 VIs = 1 AVs = 5 VR1 = 4 ΩR2 = 6 ΩR3 = 25 Ω
VB = V
6.Hard
R1​ = 6 ΩR3​ = 8 Ω+−V1​30 VR2​8 ΩAR4​12 ΩB0.25·VA​

The diamond is a voltage-controlled current source that pushes a current of 0.25·VA (in A, with VA in V) up into node B. Use nodal analysis to find the node voltage VB (measured from ground).

V1 = 30 VR1 = 6 ΩR2 = 8 ΩR3 = 8 ΩR4 = 12 Ωg = 0.25 A/V
VB = V

Answer key

  1. 1. VA = 6.824 V
  2. 2. PIs = 13.33 W
  3. 3. I3 = −0.07059 A
  4. 4. VA = 9.441 V
  5. 5. VB = 12.23 V
  6. 6. VB = 46.96 V

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