Question

A telegraph line of length 100km has a capacity of 0.01μF/km, and it carries an alternating current at 0.5kilo cycle per second. If the minimum impedance is required, then the value of the inductance that needs to be introduced in series is ______ mH.
(if π = √10)

Answer 1

The correct answer is 100
Total capacitance = 0.01 × 100 = 1 μF
ω = 500 × 2π = 1000π rad/s
$ωL = \frac{1}{ωC}$
$⇒ L = \frac{1}{ω²C}$
$= \frac{1}{10^6π^2 × 10^{-6}}$
$= \frac{1}{10}H = 100 mH$