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A 200 km long telegraph wire has capacit...

A 200 km long telegraph wire has capacity of `0.14 mu F//km`. If it carries an alternating current of `50 kc//s`, what should be the value of inductance required to be connected in series so that impedance is minimum ?

Text Solution

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Here, `l = 200 km`
Capacity ` = 0.014 mu F//km`
`:.` Total capacity of telegraph wire
`C = 0.014 xx 200 mu f = 2.8 xx 10^(-6) F`
`v = 50 kC//s = 50 xx 10^(3) C//s, L = ?`
Impedance will be minimum only at resonance, when
` v = (1)/(2 pi sqrt(LC ))`
`:. L = (1)/(4 pi^(2) v^(2) C)`
`= (1)/(4 xx (22)/(7) xx (22)/(7) xx (50 xx 10^(3))^(2) xx 2.8 xx 10^(-6))`
`L = 0.36 xx 10^(-5) H`
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