Question

A transmitter transmits at a wavelength of $300\, m$. A condenser of capacitance $2.4\, \mu F$ is being used. The value of the inductance for the resonant circuit is approximately

• A. $10^{-4}H $
• B. $10^{-6}H $
• C. $10^{-8}H $
• D. $10^{-10}H $

Answer 1

Answer: (C)

Given, $l =330\, m,$
$c=3 \times 10^{8} m / s$
Frequency, $n=\frac{c}{\lambda}=\frac{3 \times 10^{8}}{300}=10^{6} Hz$
Resonance frequency
$n =\frac{1}{2 \pi \sqrt{L C}}$
or $\sqrt{L C} =\frac{1}{2 \pi n}$
or $L C=\frac{1}{4 \pi^{2} n^{2}}$
Here, $C=2.4 \times 10^{-6} F$
$\therefore L =\frac{1}{4 \pi^{2}\left(10^{6}\right)^{2} \times 2.4 \times 10^{-6}}$
$=10^{-8} H$