Question

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