A telegraph line of length 100km has a capacity of 0 . 01 km ^ - 1...

The frequency given is $0 . 5$ kilo cycle per second $⇒ f = 500Hz ⇒ \omega = 2\pif = 1000\pi rad{s}^{- 1}$.

Total capacitance of the wire is $C = 0 . 01 \times {10}^{- 6} \times 100F$.

Impedance is minimum at resonance. Therefore, for minimum impedance

${X}_{L} = {X}_{C}$

$⇒ \omegaL = \dfrac{1}{\omegaC} ⇒ L = \dfrac{1}{{\omega}^{2}C} = \dfrac{1}{{1000}^{2} \times {\pi}^{2} \times 0 . 01 \times {10}^{- 6} \times 100} = {10}^{- 1}H = 100mH$