JEE Main 2022 · 28 Jun · Shift 1 · Physics Q60

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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 $\pi=\sqrt{10}$ )

Your answer

Answer and worked solution

Official answer: 100

Capacitance. $100\times0.01=1$ μF.

Minimum impedance at resonance: $L=\dfrac1{\omega^2C}=\dfrac1{(1000\pi)^2\times10^{-6}}=\dfrac1{10^7\times10^{-6}}=0.1$ H.

Answer: 100

Topics:LCR circuits and resonance

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JEE Main 2022 · 28 Jun · Shift 1, Physics question 60