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​ = 4 Ω+−V1​24 VR2​12 ΩIR2​AIs​1 A

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

V1 = 24 VIs = 1 AR1 = 4 ΩR2 = 12 Ω
IR2 = A
2.Easy
R1​ = 8 ΩR2​ = 6 Ω+−V1​15 VR3​5 ΩA+−V2​18 V

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

V1 = 15 VV2 = 18 VR1 = 8 ΩR2 = 6 ΩR3 = 5 Ω
VA = V
3.Medium
−+Vs​ = 5 VIs​5 AAR1​3 ΩR2​10 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 = 5 AVs = 5 VR1 = 3 ΩR2 = 10 Ω
VA = V
4.Medium
−+Vs​ = 3 VIs​5 AAR1​4 ΩR2​8 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 VB (measured from ground).

Is = 5 AVs = 3 VR1 = 4 ΩR2 = 8 Ω
VB = V
5.Hard
R1​ = 20 ΩR2​ = 6 ΩR4​ = 10 Ω+−V1​6 VR3​25 ΩAR5​6 ΩBIs​4 A+−V2​12 V

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

V1 = 6 VIs = 4 AV2 = 12 VR1 = 20 ΩR2 = 6 ΩR3 = 25 ΩR4 = 10 ΩR5 = 6 Ω
VB = V
6.Hard
R1​ = 8 ΩR3​ = 4 Ω+−V1​30 VR2​6 ΩAR4​3 ΩB0.2·VA​

The diamond is a voltage-controlled current source that pushes a current of 0.2·VA (in A, with VA in V) up into node B. Use nodal analysis to find the node voltage VB (measured from ground).

V1 = 30 VR1 = 8 ΩR2 = 6 ΩR3 = 4 ΩR4 = 3 Ωg = 0.2 A/V
VB = V

Answer key

  1. 1. IR2 = 1.25 A
  2. 2. VA = 9.915 V
  3. 3. VA = 10.38 V
  4. 4. VB = 15.33 V
  5. 5. VB = 16.59 V
  6. 6. VB = 8.294 V

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