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

Answer 1

The correct option is C ${10}^{-8}$Hz

transmitter transmits the EM waves. Frequency of the wave is same as the frequency of the LC circuit.
$\omega =2\pi f=\frac{2\pi c}{\lambda },wherec=velocityoflight\Rightarrow \omega =\frac{2\pi c}{\lambda }=2\pi \frac{3\times {10}^8}{300}=2\pi \times {10}^{6}atresonance\omega =\frac{1}{\sqrt{LC}}\Rightarrow L=\frac{1}{{\omega }^{2}C}={10}^{-8}Hz$