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  4. At 600 Hz , an inductor and capacitor have equal reactances, the ratio of the capacitive reactance to the inductive reactance at 60 Hz will be

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Q. At $ 600 \,Hz $ , an inductor and capacitor have equal reactances, the ratio of the capacitive reactance to the inductive reactance at $ 60 \,Hz $ will be

AMUAMU 2017

Solution:

At $600 \,Hz, X_C= X_L$
$\therefore \frac{1}{\omega C} = \omega L $ or $\omega^2 = \frac{1}{LC}\,\,...(i)$
At $60\,Hz, \frac{X_C}{X_L} = \frac{1}{\omega' C(\omega'L)}$
$ = \frac{1}{\omega'^2LC} = \frac{\omega^2}{\omega'^2} = \frac{V^2}{V'^2}$
(Using Eqs. $(i)$)
$ = \frac{(600)^2}{(60)^2} = \frac{100}{1}$
$\therefore X_C : X_L = 100 : 1$