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 Ω+−V1​20 VR2​10 ΩAIs​1 A

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

V1 = 20 VIs = 1 AR1 = 2 ΩR2 = 10 Ω
PIs = W
2.Easy
R1​ = 2 ΩIR1​+−V1​24 VR2​10 ΩAIs​2 A

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

V1 = 24 VIs = 2 AR1 = 2 ΩR2 = 10 Ω
IR1 = A
3.Medium
R1​8 Ω−+V1​15 VI1​R2​4 Ω+−V2​18 VR3​20 ΩA

Three branches are connected between node A and ground, as shown. Use nodal analysis to find the current I1 in branch 1, flowing up into node A in the direction of the arrow.

V1 = 15 VR1 = 8 ΩV2 = 18 VR2 = 4 ΩR3 = 20 Ω
I1 = A
4.Medium
R1​ = 20 ΩR3​ = 10 Ω+−V1​6 VR2​3 ΩAR4​2 ΩBIs​2 A

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

V1 = 6 VIs = 2 AR1 = 20 ΩR2 = 3 ΩR3 = 10 ΩR4 = 2 Ω
VB = V
5.Hard
R1​ = 8 ΩR3​ = 10 Ω+−V1​30 VR2​12 ΩAR4​8 ΩIR4​B0.25·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 current IR4 through R4 in the direction of the arrow.

V1 = 30 VR1 = 8 ΩR2 = 12 ΩR3 = 10 ΩR4 = 8 Ωg = 0.25 A/V
IR4 = A
6.Hard
R1​ = 4 ΩR2​ = 12 ΩR4​ = 2 ΩIR4​+−V1​15 VR3​8 ΩAR5​12 ΩBIs​0.5 A+−V2​9 V

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

V1 = 15 VIs = 0.5 AV2 = 9 VR1 = 4 ΩR2 = 12 ΩR3 = 8 ΩR4 = 2 ΩR5 = 12 Ω
IR4 = A

Answer key

  1. 1. PIs = 18.33 W
  2. 2. IR1 = 3.667 A
  3. 3. I1 = −2.647 A
  4. 4. VB = 3.56 V
  5. 5. IR4 = 4.773 A
  6. 6. IR4 = −0.1395 A

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