A telegraph line of length 100 , km has a cap | vedclass

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(D) The total length of the line is $l = 100 \, km$. The capacitance per unit length is $C' = 0.01 \, \mu F/km$.The total capacitance $C$ of the line

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$100$

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(D) The total length of the line is $l = 100 \, km$. The capacitance per unit length is $C' = 0.01 \, \mu F/km$.The total capacitance $C$ of the line is $C = C' 	imes l = 0.01 	imes 100 = 1 \, \mu F = 10^{-6} \, F$.The frequency $f = 0.5 \, kHz = 500 \, Hz$.The angular frequency $\omega = 2 \pi f = 2 	imes \sqrt{10} 	imes 500 = 1000 \sqrt{10} \, rad/s$.For minimum impedance in an $LCR$ circuit, the circuit must be in resonance, which occurs when inductive reactance equals capacitive reactance:$X_L = X_C$$\omega L = \frac{1}{\omega C}$$L = \frac{1}{\omega^2 C}$Substituting the values:$L = \frac{1}{(1000 \sqrt{10})^2 	imes 10^{-6}}$$L = \frac{1}{10^6 	imes 10 	imes 10^{-6}}$$L = \frac{1}{10} \, H = 0.1 \, H = 100 \, mH$.

$A$ telegraph line of length $100 \, km$ has a capacity of $0.01 \, \mu F/km$ and it carries an alternating current at $0.5 \, kHz$. If minimum impedance is required, then the value of the inductance that needs to be introduced in series is . . . . . . $mH$. (Take $\pi = \sqrt{10}$)

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