A `200km` long telegraph wire has capacitance of `0.014 mu F//km` If it carries an alternating current of `50 xx 10^(3)` Hz what should be the value of an inductance required to be connected in series in series so that impedance isw minimum .

Explanation

`C' = 0.014 muF//km`
`f =50 xx 10^(3) Hz`
Total capacitance
`C =C xx 200 =0.014 xx 200 =2.8 muF`
For impedance to be minimum
`L = (1)/(omega^(2)C) =(1)/(4pi^(2) f^(2)C)`
`(1)/(4pi^(2) xx (50 xx 10^(3))^(2) xx 2 2.8 xx 10^(-6))`
`=0.36 xx 10^(-3)H`
`0.36 mH` .