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​20 VR2​6 ΩAIs​3 A

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

V1 = 20 VIs = 3 AR1 = 12 ΩR2 = 6 Ω
PIs = W
2.Easy
R1​ = 6 Ω+−V1​8 VR2​?AIs​3 A

The node voltage at A is measured as VA = 8.5 V. Use nodal analysis to find the resistance R2.

V1 = 8 VIs = 3 AR1 = 6 ΩVA = 8.5 V
R2 = Ω
3.Medium
−+Vs​ = 8 VIx​Is​3 AAR1​2 ΩR2​3 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 current Ix through the voltage source, from A to B as shown by the arrow.

Is = 3 AVs = 8 VR1 = 2 ΩR2 = 3 Ω
Ix = A
4.Medium
R1​ = 20 ΩR3​ = 10 ΩIR3​+−V1​9 VR2​8 ΩAR4​6 ΩBIs​3 A

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

V1 = 9 VIs = 3 AR1 = 20 ΩR2 = 8 ΩR3 = 10 ΩR4 = 6 Ω
IR3 = A
5.Hard
R1​ = 30 ΩR3​ = 20 Ω+−V1​9 VR2​6 ΩAR4​30 ΩB0.25·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 node voltage VA (measured from ground).

V1 = 9 VR1 = 30 ΩR2 = 6 ΩR3 = 20 ΩR4 = 30 Ωg = 0.25 A/V
VA = V
6.Hard
R1​ = 4 ΩR2​ = 8 ΩR4​ = 6 Ω+−V1​6 VR3​10 ΩAR5​4 ΩBIs​6 A+−V2​24 V

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

V1 = 6 VIs = 6 AV2 = 24 VR1 = 4 ΩR2 = 8 ΩR3 = 10 ΩR4 = 6 ΩR5 = 4 Ω
VB = V

Answer key

  1. 1. PIs = 56 W
  2. 2. R2 = 2.914 Ω
  3. 3. Ix = 2.8 A
  4. 4. IR3 = 0.9474 A
  5. 5. VA = 4.286 V
  6. 6. VB = 20.43 V

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