JEE MAIN - Physics (2022 - 28th June Morning Shift - No. 27)
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 kilo cycle per second. If minimum impedance is required, then the value of the inductance that needs to be introduced in series is _____________ mH. (if $$\pi$$ = $$\sqrt{10}$$)
Answer
100
Explanation
Total capacitance = 0.01 $$\times$$ 100 = 1 $$\mu$$F
$$\omega$$ = 500 $$\times$$ 2$$\pi$$ = 1000$$\pi$$ rad/s
$$\omega L = {1 \over {\omega C}}$$
$$ \Rightarrow L = {1 \over {{\omega ^2}C}} = {1 \over {{{10}^6}{\pi ^2} \times {{10}^{ - 6}}}} = {1 \over {10}}H$$ = 100 mH