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​ = 3 ΩR2​ = 5 Ω+−V1​10 VR3​2 ΩA+−V2​18 V

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

V1 = 10 VV2 = 18 VR1 = 3 ΩR2 = 5 ΩR3 = 2 Ω
VA = V
2.Easy
R1​ = 8 ΩR2​ = 5 ΩIR2​+−V1​10 VR3​12 ΩA+−V2​12 V

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

V1 = 10 VV2 = 12 VR1 = 8 ΩR2 = 5 ΩR3 = 12 Ω
IR2 = A
3.Medium
R1​ = 2 ΩR3​ = 6 ΩIR3​+−V1​24 VR2​5 ΩAR4​15 ΩBIs​1 A

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

V1 = 24 VIs = 1 AR1 = 2 ΩR2 = 5 ΩR3 = 6 ΩR4 = 15 Ω
IR3 = A
4.Medium
R1​ = 10 ΩR3​ = 3 Ω+−V1​12 VR2​2 ΩAR4​3 ΩBIs​2.5 A

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

V1 = 12 VIs = 2.5 AR1 = 10 ΩR2 = 2 ΩR3 = 3 ΩR4 = 3 Ω
VB = V
5.Hard
R1​ = 8 ΩR3​ = 25 Ω+−V1​6 VR2​4 ΩAR4​25 ΩB0.1·VA​

The diamond is a voltage-controlled current source that pushes a current of 0.1·VA (in A, with VA in V) up into node B. Use nodal analysis to find the node voltage VA (measured from ground).

V1 = 6 VR1 = 8 ΩR2 = 4 ΩR3 = 25 ΩR4 = 25 Ωg = 0.1 A/V
VA = V
6.Hard
R1​ = 5 Ω−+Vs​ = 9 V+−V1​24 VR2​30 ΩAR3​10 ΩBIs​2 A

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).

V1 = 24 VIs = 2 AVs = 9 VR1 = 5 ΩR2 = 30 ΩR3 = 10 Ω
VB = V

Answer key

  1. 1. VA = 6.71 V
  2. 2. IR2 = −0.6122 A
  3. 3. IR3 = 1.433 A
  4. 4. VB = 5.348 V
  5. 5. VA = 2.174 V
  6. 6. VB = 26.7 V

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