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.

New worksheetPractise online with hints

For teachers: free to print, copy and use in class. Every new worksheet has new values and its own answer key. A link to ExamProblems on your course page is appreciated.

Name: ____________________   Date: ____________

1.Easy
R1​ = 12 ΩR2​ = 8 Ω+−V1​18 VR3​12 ΩA+−V2​8 V

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

V1 = 18 VV2 = 8 VR1 = 12 ΩR2 = 8 ΩR3 = 12 Ω
VA = V
2.Easy
R1​ = 6 ΩR2​ = 5 ΩIR2​+−V1​6 VR3​6 ΩA+−V2​24 V

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

V1 = 6 VV2 = 24 VR1 = 6 ΩR2 = 5 ΩR3 = 6 Ω
IR2 = A
3.Medium
R1​ = 4 ΩIR1​R3​ = 20 Ω+−V1​24 VR2​20 ΩAR4​10 ΩBIs​2.5 A

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

V1 = 24 VIs = 2.5 AR1 = 4 ΩR2 = 20 ΩR3 = 20 ΩR4 = 10 Ω
IR1 = A
4.Medium
R1​ = 8 ΩR3​ = 5 Ω+−V1​6 VR2​6 ΩAR4​3 ΩBIs​2.5 A

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

V1 = 6 VIs = 2.5 AR1 = 8 ΩR2 = 6 ΩR3 = 5 ΩR4 = 3 Ω
PIs = W
5.Hard
R1​ = 10 ΩR3​ = 4 Ω+−V1​15 VR2​25 ΩAR4​6 ΩBIs​?

The current source is adjusted until the node voltage at A is VA = 17 V. Use nodal analysis to find the source current Is (direction as shown).

V1 = 15 VR1 = 10 ΩR2 = 25 ΩR3 = 4 ΩR4 = 6 ΩVA = 17 V
Is = A
6.Hard
R1​ = 12 Ω−+Vs​ = 8 V+−V1​10 VR2​2 ΩAR3​25 ΩBIs​3 A

The voltage source Vₛ between A and B has its + terminal at B, so it makes VB − VA = Vₛ. Use nodal analysis with a supernode to find the node voltage VA (measured from ground).

V1 = 10 VIs = 3 AVs = 8 VR1 = 12 ΩR2 = 2 ΩR3 = 25 Ω
VA = V

Answer key

  1. 1. VA = 8.571 V
  2. 2. IR2 = −2.625 A
  3. 3. IR1 = 2.125 A
  4. 4. PIs = 15.52 W
  5. 5. Is = 4.3 A
  6. 6. VA = 5.636 V

Full step-by-step solutions: practise this topic on examproblems.com.