Question

Your little sister is building a radio from scratch. Plans call for a 500 μH inductor wound on a cardboard tube. She brings you the tube from a toilet-paper roll (12 cm long, 4.0 cm diameter), and asks how many turns she should wind on the full length of the tube.

Answer 1

N = 195 turns

Step-by-step explanation:

The inductance of the inductor, L = 500 μH = 500 * 10⁻⁶H

The length of the tube, l = 12 cm = 0.12 m

The diameter of the tube, d = 4 cm = 0.04 m

Radius, r = 0.04/2 = 0.02 m

Area of the tube, A = πr² = 0.02²π = 0.0004π m²

`\mu_(0) = 4\pi * 10^(-7)`

The inductance of a solenoid is given by:

`L = (\mu_(0)N^(2) A )/(l)`

`500 * 10^(-6) = (4\pi *10^(-7) N^(2) *4\pi *10^(-4) )/(0.12)\\500 * 10^(-6) = 0.00000001316N^(2) \\N^(2) = (500 * 10^(-6))/(0.00000001316)\\N^(2) = 37995.44\\N = √(37995.44) \\N = 194.92 turns`