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​ = 2 Ω+−V1​8 VR2​10 ΩAIs​2 A

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

V1 = 8 VIs = 2 AR1 = 2 ΩR2 = 10 Ω
PIs = W
2.Easy
R1​ = 10 ΩIR1​R2​ = 5 Ω+−V1​18 VR3​3 ΩA+−V2​12 V

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

V1 = 18 VV2 = 12 VR1 = 10 ΩR2 = 5 ΩR3 = 3 Ω
IR1 = A
3.Medium
−+Vs​ = 8 VIs​1 AAR1​20 ΩR2​2 ΩB

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 VB (measured from ground).

Is = 1 AVs = 8 VR1 = 20 ΩR2 = 2 Ω
VB = V
4.Medium
R1​ = 15 ΩR3​ = 5 Ω+−V1​12 VR2​12 ΩAR4​6 ΩBIs​1.5 A

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

V1 = 12 VIs = 1.5 AR1 = 15 ΩR2 = 12 ΩR3 = 5 ΩR4 = 6 Ω
VB = V
5.Hard
R1​ = 6 ΩR2​ = 12 ΩR4​ = 5 ΩIR4​+−V1​24 VR3​20 ΩAR5​6 ΩBIs​2.5 A+−V2​10 V

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

V1 = 24 VIs = 2.5 AV2 = 10 VR1 = 6 ΩR2 = 12 ΩR3 = 20 ΩR4 = 5 ΩR5 = 6 Ω
IR4 = A
6.Hard
R1​ = 15 ΩR3​ = 3 Ω+−V1​5 VR2​25 ΩAR4​6 ΩBIs​?

The current source is adjusted until the node voltage at A is VA = 10 V. Use nodal analysis to find the source current Is (direction as shown).

V1 = 5 VR1 = 15 ΩR2 = 25 ΩR3 = 3 ΩR4 = 6 ΩVA = 10 V
Is = A

Answer key

  1. 1. PIs = 20 W
  2. 2. IR1 = 1.137 A
  3. 3. VB = 2.545 V
  4. 4. VB = −4.132 V
  5. 5. IR4 = −1.714 A
  6. 6. Is = 2.767 A

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