A telegraph line of length 100 km has a capacity of 0.01 μ F k m − 1 and it carries an alternating current at 0.5 kilo cycle per second. If minimum impedance is required, then the value of the inducta

Question

A telegraph line of length 100 km has a capacity of 0.01 μ F k m − 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 _____ m H . (If π = 10 ​ )

TestHub · Accepted Answer

The frequency given is 0.5 kilo cycle per second ⇒ f = 500 Hz ⇒ ω = 2 π f = 1000 π r a d s − 1 . Total capacitance of the wire is C = 0.01 × 1 0 − 6 × 100 F . Impedance is minimum at resonance. Therefore, for minimum impedance X L ​ = X C ​ ⇒ ω L = ω C 1 ​ ⇒ L = ω 2 C 1 ​ = 100 0 2 × π 2 × 0.01 × 1 0 − 6 × 100 1 ​ = 1 0 − 1 H = 100 mH

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