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​ = 6 Ω+−V1​8 VR2​?AIs​2 A

The node voltage at A is measured as VA = 14.5 V. Use nodal analysis to find the resistance R2.

V1 = 8 VIs = 2 AR1 = 6 ΩVA = 14.5 V
R2 = Ω
2.Easy
R1​ = 5 Ω+−V1​18 VR2​3 ΩAIs​3 A

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

V1 = 18 VIs = 3 AR1 = 5 ΩR2 = 3 Ω
PIs = W
3.Medium
R1​15 Ω+−V1​10 VI1​R2​6 Ω−+V2​24 VR3​2 ΩA

Three branches are connected between node A and ground, as shown. Use nodal analysis to find the current I1 in branch 1, flowing up into node A in the direction of the arrow.

V1 = 10 VR1 = 15 ΩV2 = 24 VR2 = 6 ΩR3 = 2 Ω
I1 = A
4.Medium
R1​ = 2 ΩR3​ = 10 ΩIR3​+−V1​24 VR2​5 ΩAR4​4 ΩBIs​5 A

Use nodal analysis to find the current IR3 through R3 in the direction of the arrow.

V1 = 24 VIs = 5 AR1 = 2 ΩR2 = 5 ΩR3 = 10 ΩR4 = 4 Ω
IR3 = A
5.Hard
R1​ = 6 Ω−+Vs​ = 5 V+−V1​18 VR2​25 ΩAR3​5 ΩBIs​2 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 VA (measured from ground).

V1 = 18 VIs = 2 AVs = 5 VR1 = 6 ΩR2 = 25 ΩR3 = 5 Ω
VA = V
6.Hard
R1​ = 20 ΩR3​ = 5 Ω+−V1​18 VR2​5 ΩAR4​6 ΩBIs​?

The current source is adjusted until the node voltage at A is VA = 9 V. Use nodal analysis to find the source current Is (direction as shown).

V1 = 18 VR1 = 20 ΩR2 = 5 ΩR3 = 5 ΩR4 = 6 ΩVA = 9 V
Is = A

Answer key

  1. 1. R2 = 15.82 Ω
  2. 2. PIs = 37.13 W
  3. 3. I1 = 0.9697 A
  4. 4. IR3 = −0.1852 A
  5. 5. VA = 9.836 V
  6. 6. Is = 3.975 A

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