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​ = 5 Ω+−V1​18 VR2​?AIs​1 A

The node voltage at A is measured as VA = 7.5 V. Use nodal analysis to find the resistance R2.

V1 = 18 VIs = 1 AR1 = 5 ΩVA = 7.5 V
R2 = Ω
2.Easy
R1​ = 3 ΩIR1​+−V1​24 VR2​2 ΩAIs​2 A

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

V1 = 24 VIs = 2 AR1 = 3 ΩR2 = 2 Ω
IR1 = A
3.Medium
R1​15 Ω+−V1​18 VR2​6 Ω+−V2​24 VR3​15 ΩI3​A

Three branches are connected between node A and ground, as shown. Use nodal analysis to find the current I3 in branch 3, flowing up into node A in the direction of the arrow.

V1 = 18 VR1 = 15 ΩV2 = 24 VR2 = 6 ΩR3 = 15 Ω
I3 = A
4.Medium
R1​ = 8 ΩR3​ = 4 ΩIR3​+−V1​10 VR2​20 ΩAR4​15 ΩBIs​3 A

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

V1 = 10 VIs = 3 AR1 = 8 ΩR2 = 20 ΩR3 = 4 ΩR4 = 15 Ω
IR3 = A
5.Hard
R1​ = 2 ΩR2​ = 3 ΩIR2​R4​ = 12 Ω+−V1​5 VR3​12 ΩAR5​10 ΩBIs​6 A+−V2​30 V

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

V1 = 5 VIs = 6 AV2 = 30 VR1 = 2 ΩR2 = 3 ΩR3 = 12 ΩR4 = 12 ΩR5 = 10 Ω
IR2 = A
6.Hard
R1​ = 12 ΩR2​ = 3 ΩR4​ = 4 Ω+−V1​15 VR3​8 ΩAR5​12 ΩBIs​3 A−+V2​5 V

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

V1 = 15 VIs = 3 AV2 = 5 VR1 = 12 ΩR2 = 3 ΩR3 = 8 ΩR4 = 4 ΩR5 = 12 Ω
VB = V

Answer key

  1. 1. R2 = 2.419 Ω
  2. 2. IR1 = 4 A
  3. 3. I3 = −1.156 A
  4. 4. IR3 = 2.11 A
  5. 5. IR2 = −4.138 A
  6. 6. VB = 5.458 V

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