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 Ω+−V1​6 VR2​2 ΩIR2​AIs​1 A

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

V1 = 6 VIs = 1 AR1 = 3 ΩR2 = 2 Ω
IR2 = A
2.Easy
R1​ = 5 Ω+−V1​15 VR2​?AIs​1 A

The node voltage at A is measured as VA = 9.5 V. Use nodal analysis to find the resistance R2.

V1 = 15 VIs = 1 AR1 = 5 ΩVA = 9.5 V
R2 = Ω
3.Medium
R1​ = 3 ΩR3​ = 12 Ω+−V1​15 VR2​15 ΩAR4​6 ΩBIs​1.5 A

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

V1 = 15 VIs = 1.5 AR1 = 3 ΩR2 = 15 ΩR3 = 12 ΩR4 = 6 Ω
VB = V
4.Medium
R1​ = 4 ΩR3​ = 2 ΩIR3​+−V1​6 VR2​20 ΩAR4​8 ΩBIs​2 A

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

V1 = 6 VIs = 2 AR1 = 4 ΩR2 = 20 ΩR3 = 2 ΩR4 = 8 Ω
IR3 = A
5.Hard
R1​ = 20 ΩR3​ = 6 Ω+−V1​5 VR2​5 ΩAR4​15 ΩIR4​B0.05·VA​

The diamond is a voltage-controlled current source that pushes a current of 0.05·VA (in A, with VA in V) up into node B. Use nodal analysis to find the current IR4 through R4 in the direction of the arrow.

V1 = 5 VR1 = 20 ΩR2 = 5 ΩR3 = 6 ΩR4 = 15 Ωg = 0.05 A/V
IR4 = A
6.Hard
R1​ = 10 ΩR3​ = 5 Ω+−V1​24 VR2​5 ΩAR4​5 ΩBIs​?

The current source is adjusted until the node voltage at A is VA = 17 V. Use nodal analysis to find the source current Is (direction as shown).

V1 = 24 VR1 = 10 ΩR2 = 5 ΩR3 = 5 ΩR4 = 5 ΩVA = 17 V
Is = A

Answer key

  1. 1. IR2 = 1.8 A
  2. 2. R2 = 4.524 Ω
  3. 3. VB = 10.02 V
  4. 4. IR3 = −0.825 A
  5. 5. IR4 = 0.05909 A
  6. 6. Is = 8.8 A

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