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 worksheet Practise 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

Use nodal analysis to find the current I_R1 through R₁ in the direction of the arrow.

V₁ = 20 VI_s = 1 AR₁ = 10 ΩR₂ = 10 Ω

I_R1 = A

2.Easy

Use nodal analysis to find the current I_R2 through R₂ in the direction of the arrow.

V₁ = 20 VI_s = 3 AR₁ = 2 ΩR₂ = 12 Ω

I_R2 = A

3.Medium

Three branches are connected between node A and ground, as shown. Use nodal analysis to find the current I₃ in branch 3, flowing up into node A in the direction of the arrow.

V₁ = 18 VR₁ = 2 ΩV₂ = 10 VR₂ = 2 ΩV₃ = 6 VR₃ = 10 Ω

I₃ = A

4.Medium

The voltage source Vₛ between A and B has its + terminal at B, so it makes V_B − V_A = Vₛ. Use nodal analysis with a supernode to find the current I_x through the voltage source, from A to B as shown by the arrow.

I_s = 3 AV_s = 5 VR₁ = 15 ΩR₂ = 8 Ω

I_x = A

5.Hard

The current source is adjusted until the node voltage at A is V_A = 19 V. Use nodal analysis to find the source current I_s (direction as shown).

V₁ = 18 VR₁ = 30 ΩR₂ = 6 ΩR₃ = 5 ΩR₄ = 15 ΩV_A = 19 V

I_s = A

6.Hard

Use nodal analysis to find the current I_R4 through R₄ in the direction of the arrow.

V₁ = 5 VI_s = 1 AV₂ = 5 VR₁ = 2 ΩR₂ = 12 ΩR₃ = 10 ΩR₄ = 3 ΩR₅ = 8 Ω

I_R4 = A

Answer key

1. I_R1 = 0.5 A
2. I_R2 = 1.857 A
3. I₃ = −0.7273 A
4. I_x = 2.174 A
5. I_s = 5.533 A
6. I_R4 = 0.1969 A

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