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​ = 12 Ω+−V1​18 VR2​4 ΩAIs​1 A

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

V1 = 18 VIs = 1 AR1 = 12 ΩR2 = 4 Ω
PIs = W
2.Easy
R1​ = 3 ΩR2​ = 3 Ω+−V1​18 VR3​5 ΩIR3​A+−V2​20 V

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

V1 = 18 VV2 = 20 VR1 = 3 ΩR2 = 3 ΩR3 = 5 Ω
IR3 = A
3.Medium
R1​ = 20 ΩR3​ = 2 Ω+−V1​10 VR2​10 ΩAR4​3 ΩBIs​2.5 A

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

V1 = 10 VIs = 2.5 AR1 = 20 ΩR2 = 10 ΩR3 = 2 ΩR4 = 3 Ω
VA = V
4.Medium
R1​ = 8 ΩR3​ = 20 Ω+−V1​12 VR2​3 ΩAR4​3 ΩBIs​5 A

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

V1 = 12 VIs = 5 AR1 = 8 ΩR2 = 3 ΩR3 = 20 ΩR4 = 3 Ω
VB = V
5.Hard
R1​ = 6 ΩR3​ = 6 Ω+−V1​6 VR2​10 ΩAR4​30 ΩBIs​?

The current source is adjusted until the node voltage at A is VA = 11.5 V. Use nodal analysis to find the source current Is (direction as shown).

V1 = 6 VR1 = 6 ΩR2 = 10 ΩR3 = 6 ΩR4 = 30 ΩVA = 11.5 V
Is = A
6.Hard
R1​ = 3 ΩR3​ = 2 Ω+−V1​6 VR2​4 ΩAR4​6 ΩIR4​B0.25·VA​

The diamond is a voltage-controlled current source that pushes a current of 0.25·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 = 6 VR1 = 3 ΩR2 = 4 ΩR3 = 2 ΩR4 = 6 Ωg = 0.25 A/V
IR4 = A

Answer key

  1. 1. PIs = 7.5 W
  2. 2. IR3 = 2.923 A
  3. 3. VA = 5.714 V
  4. 4. VB = 13.6 V
  5. 5. Is = 2.863 A
  6. 6. IR4 = 0.72 A

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