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 ΩR2​ = 10 Ω+−V1​6 VR3​2 ΩA+−V2​6 V

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

V1 = 6 VV2 = 6 VR1 = 6 ΩR2 = 10 ΩR3 = 2 Ω
VA = V
2.Easy
R1​ = 10 ΩR2​ = 3 Ω+−V1​10 VR3​8 ΩIR3​A+−V2​18 V

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

V1 = 10 VV2 = 18 VR1 = 10 ΩR2 = 3 ΩR3 = 8 Ω
IR3 = A
3.Medium
R1​ = 15 ΩR3​ = 8 Ω+−V1​12 VR2​8 ΩAR4​12 ΩBIs​2.5 A

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

V1 = 12 VIs = 2.5 AR1 = 15 ΩR2 = 8 ΩR3 = 8 ΩR4 = 12 Ω
VB = V
4.Medium
R1​ = 6 ΩIR1​R3​ = 6 Ω+−V1​30 VR2​12 ΩAR4​3 ΩBIs​2.5 A

Use nodal analysis to find the current IR1 through R1 in the direction of the arrow.

V1 = 30 VIs = 2.5 AR1 = 6 ΩR2 = 12 ΩR3 = 6 ΩR4 = 3 Ω
IR1 = A
5.Hard
R1​ = 12 ΩR3​ = 4 Ω+−V1​24 VR2​25 ΩAR4​10 ΩBIs​?

The current source is adjusted until the node voltage at A is VA = 27 V. Use nodal analysis to find the source current Is (direction as shown).

V1 = 24 VR1 = 12 ΩR2 = 25 ΩR3 = 4 ΩR4 = 10 ΩVA = 27 V
Is = A
6.Hard
R1​ = 2 ΩR2​ = 25 ΩIR2​R4​ = 20 Ω+−V1​10 VR3​15 ΩAR5​15 ΩBIs​6 A+−V2​18 V

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

V1 = 10 VIs = 6 AV2 = 18 VR1 = 2 ΩR2 = 25 ΩR3 = 15 ΩR4 = 20 ΩR5 = 15 Ω
IR2 = A

Answer key

  1. 1. VA = 2.087 V
  2. 2. IR3 = 1.567 A
  3. 3. VB = 17.71 V
  4. 4. IR1 = 3.077 A
  5. 5. Is = 4.562 A
  6. 6. IR2 = −1.424 A

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