A radio wave of wavelength 300 m can be transmitted by a transmission center. A condenser of capacity 2.5 μF is available. The inductance of the required coil at resonance is (Given: $π^2 = 10$)

$1.00 × 10^{-8} H$

The correct answer is Option (1) → $1.00 × 10^{-8} H$

$\lambda=300\,\text{m},\; c=3\times10^8\,\text{m/s}\Rightarrow f=\frac{c}{\lambda}=10^6\,\text{Hz}$

$f=\frac{1}{2\pi\sqrt{LC}}\;\Rightarrow\; L=\frac{1}{(2\pi f)^2\,C}$

$C=2.5\,\mu\text{F}=2.5\times10^{-6}\,\text{F}$

$L=\frac{1}{4\pi^2 f^2 C}=\frac{1}{4\cdot10\cdot(10^6)^2\cdot2.5\times10^{-6}}=\frac{1}{10^8}=10^{-8}\,\text{H}$

${L=10^{-8}\,\text{H}=10\,\text{nH}}$