A telegraph line of length 100   km has a capacity of 0 . 01   μ F   km - 1 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 π = 10 )

Step-by-step solution

The frequency given is 0 . 5 kilo cycle per second ⇒ f = 500   Hz ⇒ ω = 2 π f = 1000 π   rad   s - 1 . Total capacitance of the wire is C = 0 . 01 × 10 - 6 × 100   F . Impedance is minimum at resonance. Therefore, for minimum impedance X L = X C ⇒ ω L = 1 ω C ⇒ L = 1 ω 2 C = 1 1000 2 × π 2 × 0 . 01 × 10 - 6 × 100 = 10 - 1   H = 100   mH