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​4 ΩAIs​2 A

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

V1 = 20 VIs = 2 AR1 = 8 ΩR2 = 4 Ω
PIs = W
2.Easy
R1​ = 10 ΩR2​ = 10 Ω+−V1​8 VR3​2 ΩIR3​A+−V2​24 V

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

V1 = 8 VV2 = 24 VR1 = 10 ΩR2 = 10 ΩR3 = 2 Ω
IR3 = A
3.Medium
R1​12 Ω+−V1​30 VR2​12 Ω+−V2​24 VI2​R3​6 ΩA

Three branches are connected between node A and ground, as shown. Use nodal analysis to find the current I2 in branch 2, flowing up into node A in the direction of the arrow.

V1 = 30 VR1 = 12 ΩV2 = 24 VR2 = 12 ΩR3 = 6 Ω
I2 = A
4.Medium
R1​ = 10 ΩIR1​R3​ = 8 Ω+−V1​9 VR2​4 ΩAR4​6 ΩBIs​4 A

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

V1 = 9 VIs = 4 AR1 = 10 ΩR2 = 4 ΩR3 = 8 ΩR4 = 6 Ω
IR1 = A
5.Hard
R1​ = 15 ΩR2​ = 15 ΩIR2​R4​ = 12 Ω+−V1​24 VR3​6 ΩAR5​2 ΩBIs​3 A+−V2​15 V

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

V1 = 24 VIs = 3 AV2 = 15 VR1 = 15 ΩR2 = 15 ΩR3 = 6 ΩR4 = 12 ΩR5 = 2 Ω
IR2 = A
6.Hard
R1​ = 2 ΩR3​ = 5 Ω+−V1​15 VR2​4 ΩAR4​15 ΩB0.1·VA​

The diamond is a voltage-controlled current source that pushes a current of 0.1·VA (in A, with VA in V) up into node B. Use nodal analysis to find the node voltage VB (measured from ground).

V1 = 15 VR1 = 2 ΩR2 = 4 ΩR3 = 5 ΩR4 = 15 Ωg = 0.1 A/V
VB = V

Answer key

  1. 1. PIs = 24 W
  2. 2. IR3 = 2.286 A
  3. 3. I2 = 0.875 A
  4. 4. IR1 = 0.2797 A
  5. 5. IR2 = 0.4694 A
  6. 6. VB = 11.64 V

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