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​ = 2 ΩR2​ = 10 Ω+−V1​6 VR3​12 ΩA+−V2​12 V

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

V1 = 6 VV2 = 12 VR1 = 2 ΩR2 = 10 ΩR3 = 12 Ω
VA = V
2.Easy
R1​2 Ω+−V1​10 VR2​8 Ω+−V2​18 VR3​5 Ω+−V3​6 VA

Three branches are connected between node A and ground, as shown. Use nodal analysis to find the node voltage VA.

V1 = 10 VR1 = 2 ΩV2 = 18 VR2 = 8 ΩV3 = 6 VR3 = 5 Ω
VA = V
3.Medium
R1​ = 3 ΩIR1​R3​ = 20 Ω+−V1​6 VR2​3 ΩAR4​10 ΩBIs​2.5 A

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

V1 = 6 VIs = 2.5 AR1 = 3 ΩR2 = 3 ΩR3 = 20 ΩR4 = 10 Ω
IR1 = A
4.Medium
−+Vs​ = 9 VIs​3 AAR1​5 ΩR2​5 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 node voltage VA (measured from ground).

Is = 3 AVs = 9 VR1 = 5 ΩR2 = 5 Ω
VA = V
5.Hard
R1​ = 20 Ω+−Vs​ = 10 VIx​+−V1​6 VR2​6 ΩAR3​3 ΩBIs​6 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 = 6 VIs = 6 AVs = 10 VR1 = 20 ΩR2 = 6 ΩR3 = 3 Ω
Ix = A
6.Hard
R1​ = 3 ΩR2​ = 12 ΩR4​ = 20 ΩIR4​+−V1​36 VR3​10 ΩAR5​15 ΩBIs​1 A−+V2​15 V

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

V1 = 36 VIs = 1 AV2 = 15 VR1 = 3 ΩR2 = 12 ΩR3 = 10 ΩR4 = 20 ΩR5 = 15 Ω
IR4 = A

Answer key

  1. 1. VA = 6.146 V
  2. 2. VA = 10.24 V
  3. 3. IR1 = 0.6508 A
  4. 4. VA = 3 V
  5. 5. Ix = −3.495 A
  6. 6. IR4 = 1.336 A

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