Question

A transmitting station releases waves of wavelength $960\text{m}$. A capacitor of capacitance $2.56\mu \text{F}$ is used in the resonant circuit. The self inductance of the coil necessary for resonance is _______$\times {10}^{-8}\text{H}$.

Answer 1

At resonance,
${\omega }_o=\frac{1}{\sqrt{LC}}$

$\Rightarrow 2\pi f=\frac{1}{\sqrt{LC}}$

$\Rightarrow L=\frac{1}{4{\pi }^2{f}^{2}C}=\frac{1}{4{\pi }^2(c/\lambda {)}^{2}C}$

$\Rightarrow L=\frac{1}{4{\pi }^2\times (3\times {10}^8/960{)}^2\times 2.56\times {10}^{-6}}$

$\Rightarrow L=10\times {10}^{-8}\text{H}$