Question

A broadcasting centre broadcasts at 300 metre band. A capacitor of capacitance 2.5$\mu$F is available. The value of the inductance required for resonant circuit is nearly

• A. $1\times {10}^{-4}H$
• B. $1\times {10}^{-8}H$
• C. $1\times {10}^{-6}H$
• D. $1\times {10}^{-2}H$

Answer 1

The correct option is B $1\times {10}^{-8}H$

$c=\lambda \nu atresonance$

$\nu =\frac{c}{\lambda }=\frac{1}{2\pi \sqrt{LC}}$

$\sqrt{LC}=\frac{300}{3\times {10}^8\times 2\pi }=\frac{{10}^{-6}}{2\pi }$
$LC=\frac{{10}^{-12}}{4{\pi }^2}$
$L=\frac{{10}^{-12}}{2.5\times {10}^{-6}\times 4\times 9.87}=\frac{{10}^{-6}}{98.7}\cong {10}^{-8}H$