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​24 VR2​?AIs​3 A

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

V1 = 24 VIs = 3 AR1 = 6 ΩVA = 14.5 V
R2 = Ω
2.Easy
R1​ = 4 Ω+−V1​12 VR2​12 ΩIR2​AIs​2 A

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

V1 = 12 VIs = 2 AR1 = 4 ΩR2 = 12 Ω
IR2 = A
3.Medium
R1​ = 20 ΩR3​ = 20 Ω+−V1​9 VR2​15 ΩAR4​10 ΩBIs​2.5 A

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

V1 = 9 VIs = 2.5 AR1 = 20 ΩR2 = 15 ΩR3 = 20 ΩR4 = 10 Ω
VA = V
4.Medium
R1​10 Ω−+V1​30 VR2​3 Ω+−V2​18 VR3​8 Ω+−V3​24 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 = 30 VR1 = 10 ΩV2 = 18 VR2 = 3 ΩV3 = 24 VR3 = 8 Ω
I3 = A
5.Hard
R1​ = 15 ΩR2​ = 10 ΩR4​ = 4 ΩIR4​+−V1​5 VR3​3 ΩAR5​3 ΩBIs​2.5 A+−V2​12 V

Use nodal analysis to find the current IR4 through R4 in the direction of the arrow.

V1 = 5 VIs = 2.5 AV2 = 12 VR1 = 15 ΩR2 = 10 ΩR3 = 3 ΩR4 = 4 ΩR5 = 3 Ω
IR4 = A
6.Hard
R1​ = 4 ΩR2​ = 12 ΩR4​ = 5 Ω+−V1​24 VR3​25 ΩAR5​20 ΩBIs​2.5 A−+V2​5 V

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

V1 = 24 VIs = 2.5 AV2 = 5 VR1 = 4 ΩR2 = 12 ΩR3 = 25 ΩR4 = 5 ΩR5 = 20 Ω
VB = V

Answer key

  1. 1. R2 = 3.164 Ω
  2. 2. IR2 = 1.25 A
  3. 3. VA = 8.556 V
  4. 4. I3 = 1.657 A
  5. 5. IR4 = −0.902 A
  6. 6. VB = 9.021 V

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