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

\(C =2.56 \mu F =2.56 \times 10^{-6} F\)

\(c=3 \times 10^{8} m / s\)

\(L =?\)

Now at resonance, \(\omega_{0}=\frac{1}{\sqrt{L C}}\)

[Resoant frequency]

\(2 \pi f _{0}=\frac{1}{\sqrt{ LC }}\)

On substituting \(f _{0}=\frac{ c }{\lambda},\) we have \(2 \pi \frac{ c }{\lambda}=\frac{1}{\sqrt{ LC }}\)

Squaring both sides : \(4 \pi^{2} \frac{ c ^{2}}{\lambda^{2}}=\frac{1}{ LC }\)

\(=\frac{4 \times 10 \times\left(3 \times 10^{8}\right)^{2}}{(960)^{2}}=\frac{1}{ L \times 2.56 \times 10^{-6}}\)

\(\Rightarrow \frac{1}{L}=\frac{4 \times 10 \times 9 \times 10^{16} \times 2.56 \times 10^{-6}}{960 \times 960}\)

\(\Rightarrow L =10 \times 10^{-8} H\)