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 Ω+−V1​15 VR2​?AIs​3 A

The node voltage at A is measured as VA = 20.5 V. Use nodal analysis to find the resistance R2.

V1 = 15 VIs = 3 AR1 = 4 ΩVA = 20.5 V
R2 = Ω
2.Easy
R1​ = 5 Ω+−V1​8 VR2​4 ΩIR2​AIs​1 A

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

V1 = 8 VIs = 1 AR1 = 5 ΩR2 = 4 Ω
IR2 = A
3.Medium
R1​ = 10 ΩIR1​R3​ = 12 Ω+−V1​30 VR2​3 ΩAR4​5 ΩBIs​5 A

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

V1 = 30 VIs = 5 AR1 = 10 ΩR2 = 3 ΩR3 = 12 ΩR4 = 5 Ω
IR1 = A
4.Medium
R1​ = 4 ΩR3​ = 8 Ω+−V1​18 VR2​2 ΩAR4​10 ΩBIs​3 A

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

V1 = 18 VIs = 3 AR1 = 4 ΩR2 = 2 ΩR3 = 8 ΩR4 = 10 Ω
VA = V
5.Hard
R1​ = 4 ΩR2​ = 4 ΩR4​ = 2 Ω+−V1​12 VR3​20 ΩAR5​6 ΩBIs​0.5 A+−V2​15 V

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

V1 = 12 VIs = 0.5 AV2 = 15 VR1 = 4 ΩR2 = 4 ΩR3 = 20 ΩR4 = 2 ΩR5 = 6 Ω
VB = V
6.Hard
R1​ = 8 ΩR3​ = 5 Ω+−V1​30 VR2​6 ΩAR4​8 ΩBIs​?

The current source is adjusted until the node voltage at A is VA = 29 V. Use nodal analysis to find the source current Is (direction as shown).

V1 = 30 VR1 = 8 ΩR2 = 6 ΩR3 = 5 ΩR4 = 8 ΩVA = 29 V
Is = A

Answer key

  1. 1. R2 = 12.62 Ω
  2. 2. IR2 = 0.3333 A
  3. 3. IR1 = 2.092 A
  4. 4. VA = 7.655 V
  5. 5. VB = 11.66 V
  6. 6. Is = 11.28 A

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