A transmitting station releases waves of wavelength 960m . A...

$\lambda = 960m$

$C = 2 . 56\muF = 2 . 56 \times {10}^{- 6}F$

$c = 3 \times {10}^{8}m{s}^{- 1}$

$L = ?$

Now at resonance, ${\omega}_{0} = \dfrac{1}{\sqrt{LC}}$ [Resonant frequency]

$2\pi{f}_{0} = \dfrac{1}{\sqrt{LC}}$

On substituting ${f}_{0} = \dfrac{c}{\lambda},$ we have $2\pi\dfrac{c}{\lambda} = \dfrac{1}{\sqrt{LC}}$

On substituting ${f}_{0} = \dfrac{c}{\lambda},$ we have $2\pi\dfrac{c}{\lambda} = \dfrac{1}{\sqrt{LC}}$

Squaring both sides: $4{\pi}^{2}\dfrac{{c}^{2}}{{\lambda}^{2}} = \dfrac{1}{LC}$

$= \dfrac{4 \times 10 \times {\left(3 \times {10}^{8}\right)}^{2}}{{\left(960\right)}^{2}} = \dfrac{1}{L \times 2 . 56 \times {10}^{- 6}}$

$⇒ \dfrac{1}{L} = \dfrac{4 \times 10 \times 9 \times {10}^{16} \times 2 . 56 \times {10}^{- 6}}{960 \times 960}$

$⇒ L = 10 \times {10}^{- 8}H$