Question

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

• A. $0.5\text{m}$
• B. $5\text{m}$
• C. $190\text{m}$
• D. $19\text{m}$
  

Answer 1

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

Given,

$L=1\mu \text{H};C=0.01\mu \text{F}$

For an LC the resonant frequency of oscillation is,

$\omega =\frac{1}{\sqrt{LC}}$

$2\pi f=\frac{1}{\sqrt{1\times {10}^{-6}\times 1\times {10}^{-8}}}$

$f=\frac{{10}^7}{2\pi }$

$\because c=\lambda f$

$\lambda =\frac{c}{f}$

$\lambda =\frac{3\times {10}^8}{{10}^7}\times 2\pi =60\pi \approx 190\text{m}$

<!--td {border: 1px solid #ccc;}br {mso-data-placement:same-cell;}--> Hence, $\left(C\right)$ is the correct answer.