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​12 VR2​8 Ω+−V2​15 VR3​8 Ω+−V3​18 VA

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

V1 = 12 VR1 = 2 ΩV2 = 15 VR2 = 8 ΩV3 = 18 VR3 = 8 Ω
VA = V
2.Easy
R1​ = 4 Ω+−V1​6 VR2​?AIs​1 A

The node voltage at A is measured as VA = 3.5 V. Use nodal analysis to find the resistance R2.

V1 = 6 VIs = 1 AR1 = 4 ΩVA = 3.5 V
R2 = Ω
3.Medium
R1​ = 2 ΩR3​ = 4 ΩIR3​+−V1​18 VR2​8 ΩAR4​20 ΩBIs​4 A

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

V1 = 18 VIs = 4 AR1 = 2 ΩR2 = 8 ΩR3 = 4 ΩR4 = 20 Ω
IR3 = A
4.Medium
R1​ = 8 ΩR3​ = 2 Ω+−V1​15 VR2​8 ΩAR4​15 ΩBIs​2 A

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

V1 = 15 VIs = 2 AR1 = 8 ΩR2 = 8 ΩR3 = 2 ΩR4 = 15 Ω
VA = V
5.Hard
R1​ = 2 ΩR2​ = 25 ΩR4​ = 8 ΩIR4​+−V1​18 VR3​3 ΩAR5​3 ΩBIs​3 A−+V2​18 V

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

V1 = 18 VIs = 3 AV2 = 18 VR1 = 2 ΩR2 = 25 ΩR3 = 3 ΩR4 = 8 ΩR5 = 3 Ω
IR4 = A
6.Hard
R1​ = 25 ΩIR1​+−Vs​ = 9 V+−V1​15 VR2​10 ΩAR3​20 ΩBIs​6 A

The voltage source Vₛ between A and B has its + terminal at A, so it makes VA − VB = Vₛ. Use nodal analysis with a supernode to find the current IR1 through R1 in the direction of the arrow.

V1 = 15 VIs = 6 AVs = 9 VR1 = 25 ΩR2 = 10 ΩR3 = 20 Ω
IR1 = A

Answer key

  1. 1. VA = 13.5 V
  2. 2. R2 = 2.154 Ω
  3. 3. IR3 = −2.563 A
  4. 4. VA = 11.79 V
  5. 5. IR4 = 2.543 A
  6. 6. IR1 = −0.8842 A

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