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​5 ΩAIs​1 A

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

V1 = 20 VIs = 1 AR1 = 8 ΩR2 = 5 Ω
PIs = W
2.Easy
R1​ = 12 Ω+−V1​10 VR2​10 ΩIR2​AIs​3 A

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

V1 = 10 VIs = 3 AR1 = 12 ΩR2 = 10 Ω
IR2 = A
3.Medium
R1​4 Ω−+V1​18 VR2​4 Ω+−V2​12 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 = 18 VR1 = 4 ΩV2 = 12 VR2 = 4 ΩR3 = 6 Ω
I2 = A
4.Medium
R1​ = 15 ΩIR1​R3​ = 4 Ω+−V1​30 VR2​4 ΩAR4​3 ΩBIs​1.5 A

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

V1 = 30 VIs = 1.5 AR1 = 15 ΩR2 = 4 ΩR3 = 4 ΩR4 = 3 Ω
IR1 = A
5.Hard
R1​ = 30 ΩR2​ = 3 ΩR4​ = 25 ΩIR4​+−V1​5 VR3​6 ΩAR5​8 ΩBIs​2.5 A+−V2​18 V

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

V1 = 5 VIs = 2.5 AV2 = 18 VR1 = 30 ΩR2 = 3 ΩR3 = 6 ΩR4 = 25 ΩR5 = 8 Ω
IR4 = A
6.Hard
R1​ = 30 ΩR3​ = 2 Ω+−V1​5 VR2​4 ΩAR4​6 ΩIR4​B0.1·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 current IR4 through R4 in the direction of the arrow.

V1 = 5 VR1 = 30 ΩR2 = 4 ΩR3 = 2 ΩR4 = 6 Ωg = 0.1 A/V
IR4 = A

Answer key

  1. 1. PIs = 10.77 W
  2. 2. IR2 = −1.182 A
  3. 3. I2 = 3.563 A
  4. 4. IR1 = 1.617 A
  5. 5. IR4 = −0.2615 A
  6. 6. IR4 = 0.075 A

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