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​ = 8 Ω+−V1​15 VR2​?AIs​3 A

The node voltage at A is measured as VA = 15.5 V. Use nodal analysis to find the resistance R2.

V1 = 15 VIs = 3 AR1 = 8 ΩVA = 15.5 V
R2 = Ω
2.Easy
R1​ = 4 Ω+−V1​20 VR2​4 ΩAIs​3 A

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

V1 = 20 VIs = 3 AR1 = 4 ΩR2 = 4 Ω
VA = V
3.Medium
R1​ = 8 ΩR3​ = 20 Ω+−V1​18 VR2​4 ΩAR4​10 ΩBIs​1.5 A

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

V1 = 18 VIs = 1.5 AR1 = 8 ΩR2 = 4 ΩR3 = 20 ΩR4 = 10 Ω
PIs = W
4.Medium
R1​ = 15 ΩR3​ = 4 Ω+−V1​30 VR2​15 ΩAR4​10 ΩBIs​2.5 A

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

V1 = 30 VIs = 2.5 AR1 = 15 ΩR2 = 15 ΩR3 = 4 ΩR4 = 10 Ω
VB = V
5.Hard
R1​ = 12 ΩR2​ = 25 ΩR4​ = 10 ΩIR4​+−V1​6 VR3​15 ΩAR5​8 ΩBIs​1.5 A+−V2​5 V

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

V1 = 6 VIs = 1.5 AV2 = 5 VR1 = 12 ΩR2 = 25 ΩR3 = 15 ΩR4 = 10 ΩR5 = 8 Ω
IR4 = A
6.Hard
R1​ = 20 ΩR3​ = 5 Ω+−V1​15 VR2​4 ΩAR4​6 ΩBIs​?

The current source is adjusted until the node voltage at A is VA = 6 V. Use nodal analysis to find the source current Is (direction as shown).

V1 = 15 VR1 = 20 ΩR2 = 4 ΩR3 = 5 ΩR4 = 6 ΩVA = 6 V
Is = A

Answer key

  1. 1. R2 = 5.277 Ω
  2. 2. VA = 16 V
  3. 3. PIs = 18.37 W
  4. 4. VB = −6.395 V
  5. 5. IR4 = 0.3205 A
  6. 6. Is = 2.925 A

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