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​ = 8 Ω+−V1​20 VR2​8 ΩAIs​1 A

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

V1 = 20 VIs = 1 AR1 = 8 ΩR2 = 8 Ω
VA = V
2.Easy
R1​ = 10 Ω+−V1​18 VR2​4 ΩIR2​AIs​1 A

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

V1 = 18 VIs = 1 AR1 = 10 ΩR2 = 4 Ω
IR2 = A
3.Medium
R1​ = 4 ΩIR1​R3​ = 8 Ω+−V1​12 VR2​15 ΩAR4​6 ΩBIs​1.5 A

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

V1 = 12 VIs = 1.5 AR1 = 4 ΩR2 = 15 ΩR3 = 8 ΩR4 = 6 Ω
IR1 = A
4.Medium
R1​ = 15 ΩR3​ = 4 Ω+−V1​9 VR2​20 ΩAR4​8 ΩBIs​5 A

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

V1 = 9 VIs = 5 AR1 = 15 ΩR2 = 20 ΩR3 = 4 ΩR4 = 8 Ω
PIs = W
5.Hard
R1​ = 15 Ω+−Vs​ = 8 VIx​+−V1​15 VR2​5 ΩAR3​12 ΩBIs​5 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 Ix through the voltage source, from A to B as shown by the arrow.

V1 = 15 VIs = 5 AVs = 8 VR1 = 15 ΩR2 = 5 ΩR3 = 12 Ω
Ix = A
6.Hard
R1​ = 2 ΩR2​ = 20 ΩR4​ = 25 ΩIR4​+−V1​30 VR3​25 ΩAR5​8 ΩBIs​3 A−+V2​18 V

Use nodal analysis to find the current IR4 through R4 in the direction of the arrow.

V1 = 30 VIs = 3 AV2 = 18 VR1 = 2 ΩR2 = 20 ΩR3 = 25 ΩR4 = 25 ΩR5 = 8 Ω
IR4 = A

Answer key

  1. 1. VA = 14 V
  2. 2. IR2 = 2 A
  3. 3. IR1 = 1.482 A
  4. 4. PIs = 132.2 W
  5. 5. Ix = −4.079 A
  6. 6. IR4 = 0.2552 A

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