Question

An LC resonant circuit contains a $400pF$ capacitor and a $100\mu H$ inductor. It is set into oscillation coupled to an antenna. The wavelength of the radiated electromagnetic waves is

• A. 377.14 $mm$
• B. 377.14 $m$
• C. 377.14 $cm$
• D. 3.7714 $cm$

Answer 1

The correct option is B 377.14 $m$

We know that frequency of the LC oscillations is given by

$\nu =\frac{1}{2\pi \sqrt{\mathrm{LC}}}=\frac{1}{2\pi \sqrt{100\times {10}^{-6}\times 400\times {10}^{-12}}}=\frac{1}{4\pi \times {10}^{-7}}$Now to calculate the wavelength
$\lambda =\frac{c}{\nu }(wherec=speedoflight)=\frac{3\times {10}^8}{1}\times 4\pi \times {10}^{-7}=377m$