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 Ω+−V1​15 VR2​10 Ω+−V2​18 VR3​8 ΩA

Three branches are connected between node A and ground, as shown. Use nodal analysis to find the node voltage VA.

V1 = 15 VR1 = 12 ΩV2 = 18 VR2 = 10 ΩR3 = 8 Ω
VA = V
2.Easy
R1​ = 5 Ω+−V1​18 VR2​?AIs​2 A

The node voltage at A is measured as VA = 11.5 V. Use nodal analysis to find the resistance R2.

V1 = 18 VIs = 2 AR1 = 5 ΩVA = 11.5 V
R2 = Ω
3.Medium
R1​4 Ω+−V1​18 VR2​4 Ω+−V2​12 VR3​8 Ω+−V3​12 VI3​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 = 4 ΩV2 = 12 VR2 = 4 ΩV3 = 12 VR3 = 8 Ω
I3 = A
4.Medium
R1​ = 3 ΩR3​ = 3 Ω+−V1​9 VR2​8 ΩAR4​3 ΩBIs​1 A

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

V1 = 9 VIs = 1 AR1 = 3 ΩR2 = 8 ΩR3 = 3 ΩR4 = 3 Ω
VA = V
5.Hard
R1​ = 5 ΩIR1​R2​ = 10 ΩR4​ = 30 Ω+−V1​24 VR3​5 ΩAR5​12 ΩBIs​4 A+−V2​12 V

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

V1 = 24 VIs = 4 AV2 = 12 VR1 = 5 ΩR2 = 10 ΩR3 = 5 ΩR4 = 30 ΩR5 = 12 Ω
IR1 = A
6.Hard
R1​ = 30 ΩR2​ = 20 ΩR4​ = 12 ΩIR4​+−V1​15 VR3​4 ΩAR5​8 ΩBIs​2 A−+V2​6 V

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

V1 = 15 VIs = 2 AV2 = 6 VR1 = 30 ΩR2 = 20 ΩR3 = 4 ΩR4 = 12 ΩR5 = 8 Ω
IR4 = A

Answer key

  1. 1. VA = 9.892 V
  2. 2. R2 = 3.485 Ω
  3. 3. I3 = −0.3 A
  4. 4. VA = 5.6 V
  5. 5. IR1 = 1.79 A
  6. 6. IR4 = 1.023 A

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