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 ΩR2​ = 6 Ω+−V1​20 VR3​10 ΩIR3​A+−V2​24 V

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

V1 = 20 VV2 = 24 VR1 = 4 ΩR2 = 6 ΩR3 = 10 Ω
IR3 = A
2.Easy
R1​ = 5 Ω+−V1​20 VR2​?AIs​1 A

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

V1 = 20 VIs = 1 AR1 = 5 ΩVA = 14.5 V
R2 = Ω
3.Medium
R1​2 Ω−+V1​30 VR2​5 Ω+−V2​9 VR3​8 ΩI3​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 = 30 VR1 = 2 ΩV2 = 9 VR2 = 5 ΩR3 = 8 Ω
I3 = A
4.Medium
R1​ = 3 ΩR3​ = 10 Ω+−V1​9 VR2​2 ΩAR4​4 ΩBIs​3 A

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

V1 = 9 VIs = 3 AR1 = 3 ΩR2 = 2 ΩR3 = 10 ΩR4 = 4 Ω
VB = V
5.Hard
R1​ = 30 ΩR3​ = 25 Ω+−V1​6 VR2​5 ΩAR4​20 ΩBIs​?

The current source is adjusted until the node voltage at A is VA = 5 V. Use nodal analysis to find the source current Is (direction as shown).

V1 = 6 VR1 = 30 ΩR2 = 5 ΩR3 = 25 ΩR4 = 20 ΩVA = 5 V
Is = A
6.Hard
R1​ = 30 ΩR2​ = 25 ΩIR2​R4​ = 5 Ω+−V1​30 VR3​4 ΩAR5​10 ΩBIs​1.5 A+−V2​15 V

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

V1 = 30 VIs = 1.5 AV2 = 15 VR1 = 30 ΩR2 = 25 ΩR3 = 4 ΩR4 = 5 ΩR5 = 10 Ω
IR2 = A

Answer key

  1. 1. IR3 = 1.742 A
  2. 2. R2 = 6.905 Ω
  3. 3. I3 = 2 A
  4. 4. VB = 9.789 V
  5. 5. Is = 2.425 A
  6. 6. IR2 = −0.36 A

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