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​ = 5 ΩR2​ = 12 Ω+−V1​15 VR3​6 ΩIR3​A+−V2​10 V

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

V1 = 15 VV2 = 10 VR1 = 5 ΩR2 = 12 ΩR3 = 6 Ω
IR3 = A
2.Easy
R1​ = 12 Ω+−V1​15 VR2​?AIs​3 A

The node voltage at A is measured as VA = 32.5 V. Use nodal analysis to find the resistance R2.

V1 = 15 VIs = 3 AR1 = 12 ΩVA = 32.5 V
R2 = Ω
3.Medium
−+Vs​ = 5 VIx​Is​1 AAR1​6 ΩR2​20 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 = 1 AVs = 5 VR1 = 6 ΩR2 = 20 Ω
Ix = A
4.Medium
R1​ = 8 ΩR3​ = 8 Ω+−V1​24 VR2​6 ΩAR4​8 ΩBIs​2.5 A

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

V1 = 24 VIs = 2.5 AR1 = 8 ΩR2 = 6 ΩR3 = 8 ΩR4 = 8 Ω
PIs = W
5.Hard
R1​ = 12 ΩR3​ = 30 Ω+−V1​18 VR2​8 ΩAR4​5 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 = 18 VR1 = 12 ΩR2 = 8 ΩR3 = 30 ΩR4 = 5 Ωg = 0.2 A/V
VB = V
6.Hard
R1​ = 20 ΩR2​ = 10 ΩR4​ = 4 Ω+−V1​10 VR3​20 ΩAR5​20 ΩBIs​6 A+−V2​36 V

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

V1 = 10 VIs = 6 AV2 = 36 VR1 = 20 ΩR2 = 10 ΩR3 = 20 ΩR4 = 4 ΩR5 = 20 Ω
VB = V

Answer key

  1. 1. IR3 = 1.42 A
  2. 2. R2 = 21.08 Ω
  3. 3. Ix = 0.4231 A
  4. 4. PIs = 40 W
  5. 5. VB = 7.2 V
  6. 6. VB = 43.57 V

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