Chapter 21, Problem 86GP

To determine

To find the inductance $l$ of the primary of a transformer whose input is $220 V at 60.0Hz$.

Answer to Problem 86GP

Solution:

The inductance is obtained as $93.0mH$.

Explanation of Solution

Given info:

$\omega$ is the angular frequency and L is the inductance.

Formula used:

$X_L=\omega L$

Calculation:

The expression for reactance of an inductor is given as

$X_L=\omega L\mathrm{............}\left(1\right)$

$\begin{array}{l}\omega =2\pi f\\ X_L=\left(2\pi f\right)L\mathrm{..................}\left(2\right)\\ X_L=\frac{V}{I}\mathrm{...........................}\left(3\right)\\ \frac{V}{I}=\left(2\pi f\right)L\\ L=\frac{V}{2\pi fI}\mathrm{...........................}\left(4\right)\\ L=\frac{220V}{2\pi \left(60.0Hz\right)\left(6.3A\right)}\\ =\left(93.0\times {10}^{-3}H\right)\left(\frac{1.0mH}{{10}^{-3}H}\right)\\ =93.0mH\end{array}$