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​ = 8 Ω+−V1​15 VR3​6 ΩIR3​A+−V2​20 V

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

V1 = 15 VV2 = 20 VR1 = 2 ΩR2 = 8 ΩR3 = 6 Ω
IR3 = A
2.Easy
R1​ = 12 Ω+−V1​8 VR2​?AIs​1 A

The node voltage at A is measured as VA = 2.5 V. Use nodal analysis to find the resistance R2.

V1 = 8 VIs = 1 AR1 = 12 ΩVA = 2.5 V
R2 = Ω
3.Medium
R1​6 Ω+−V1​6 VI1​R2​10 Ω+−V2​30 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 = 6 VR1 = 6 ΩV2 = 30 VR2 = 10 ΩR3 = 20 Ω
I1 = A
4.Medium
R1​ = 6 ΩIR1​R3​ = 8 Ω+−V1​18 VR2​10 ΩAR4​10 ΩBIs​2 A

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

V1 = 18 VIs = 2 AR1 = 6 ΩR2 = 10 ΩR3 = 8 ΩR4 = 10 Ω
IR1 = A
5.Hard
R1​ = 12 ΩR2​ = 10 ΩR4​ = 4 Ω+−V1​30 VR3​20 ΩAR5​12 ΩBIs​1 A+−V2​12 V

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

V1 = 30 VIs = 1 AV2 = 12 VR1 = 12 ΩR2 = 10 ΩR3 = 20 ΩR4 = 4 ΩR5 = 12 Ω
VA = V
6.Hard
R1​ = 4 ΩR3​ = 6 Ω+−V1​30 VR2​3 ΩAR4​30 ΩB0.25·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 node voltage VA (measured from ground).

V1 = 30 VR1 = 4 ΩR2 = 3 ΩR3 = 6 ΩR4 = 30 Ωg = 0.25 A/V
VA = V

Answer key

  1. 1. IR3 = 2.105 A
  2. 2. R2 = 1.714 Ω
  3. 3. I1 = −1.105 A
  4. 4. IR1 = 0.8736 A
  5. 5. VA = 14.09 V
  6. 6. VA = 18.62 V

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