Question

A $200km$ long telegraph wire has a capacitance of $0.014\mu F/km$. If it carries an ac of $5kHz$, what should be the inductance required to be connected in series, so that the impedance is minimum?
Take $\pi =\sqrt{10}$

Answer 1

For minimum impedance

$\begin{array}{c}{X}_L=X_C\\ \omega L=\frac{1}{\omega C}\\ L=\frac{1}{{\omega }^{2}C}=\frac{1}{{\left(2\pi f\right)}^{2}C}\\ For1kmC=0.14\mu F\\ For200kmC=0.14\times 200\mu F\\ L=\frac{1}{\left(2\times 3.14\times 5\times {10}^3\right)\times 0.014\times 200}=0.36mH\end{array}$