Question

What is the reactance of an air core solenoid of length 6.00 cm, radius 1.20 cm, and 247 turns at a frequency of 21.0 kHz?

Answer 1

First, we find the inductance of the solenoid, and the we find the reactance.

The inductance of a solenoid is given by

$L=\frac{\mu N^2 A}{l}$

where , the permeability of air

u = 47 x 10-'H/m

is the number of turns

is the cross-sectional area, equal to $A=\pi r^2=\pi \times (1.2\times 10^{-2})^2=4.524\times 10^{-4}\mathrm{m^2}$

and is the length.

Putting in our values, we get

$\\ L=\frac{(4\pi \times 10^{-7})\times 247^2\times 4.524\times 10^{-4} }{6\times 10^{-2}} \\ L=5.78\times 10^{-4}\mathrm{H}$

Now, we can use the formula for reactance.

$X_L=2\pi fL$

Putting in our values, we get

$\\ X_L=2\pi\times 21\times 10^3\times 5.78\times 10^{-4} \\ X_L=76.265\Omega$