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​10 VR2​6 Ω+−V2​8 VR3​8 ΩA

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

V1 = 10 VR1 = 2 ΩV2 = 8 VR2 = 6 ΩR3 = 8 Ω
VA = V
2.Easy
R1​ = 3 ΩIR1​R2​ = 2 Ω+−V1​12 VR3​8 ΩA+−V2​6 V

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

V1 = 12 VV2 = 6 VR1 = 3 ΩR2 = 2 ΩR3 = 8 Ω
IR1 = A
3.Medium
−+Vs​ = 6 VIs​2 AAR1​8 ΩR2​15 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 VA (measured from ground).

Is = 2 AVs = 6 VR1 = 8 ΩR2 = 15 Ω
VA = V
4.Medium
R1​ = 4 ΩR3​ = 10 Ω+−V1​30 VR2​3 ΩAR4​15 ΩBIs​1.5 A

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

V1 = 30 VIs = 1.5 AR1 = 4 ΩR2 = 3 ΩR3 = 10 ΩR4 = 15 Ω
PIs = W
5.Hard
R1​ = 10 ΩIR1​+−Vs​ = 10 V+−V1​6 VR2​25 ΩAR3​15 ΩBIs​3 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 = 6 VIs = 3 AVs = 10 VR1 = 10 ΩR2 = 25 ΩR3 = 15 Ω
IR1 = A
6.Hard
R1​ = 20 ΩR2​ = 10 ΩR4​ = 30 Ω+−V1​10 VR3​3 ΩAR5​25 ΩBIs​6 A+−V2​9 V

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

V1 = 10 VIs = 6 AV2 = 9 VR1 = 20 ΩR2 = 10 ΩR3 = 3 ΩR4 = 30 ΩR5 = 25 Ω
VA = V

Answer key

  1. 1. VA = 8 V
  2. 2. IR1 = 1.565 A
  3. 3. VA = 8.348 V
  4. 4. PIs = 25.63 W
  5. 5. IR1 = −1.465 A
  6. 6. VA = 9.714 V

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