Question

An $LC$ circuit contains inductance $L=1\mu \text{H}$ and capacitance $C=0.01\mu \text{F}$. The wavelength of electromagnetic wave generated is nearly

• A. $0.5\text{m}$
• B. $5\text{m}$
• C. $190\text{m}$
• D. $30\text{m}$

Answer 1

The correct option is C $190\text{m}$

For resonant frequency, we can write
$\omega =\frac{1}{\sqrt{LC}}=\frac{1}{\sqrt{{10}^{-6}\times {10}^{-8}}}={10}^7$
$f=\frac{\omega }{2\pi }$
$f=\frac{{10}^7}{2\pi }$
Velocity of the wave
$\therefore v=f\lambda \Rightarrow \lambda =\frac{v}{f}$
$\lambda =\frac{3\times {10}^8}{{10}^7}\times 2\pi =60\pi =188.57\approx 190\text{m}$
Hence, option (C) is correct.