Verified Solution • 2025–26 Session moderate

QJEEM22Ph1c4a: JEE Main 2022 Physics - Class 12 JEEM22Ph1c4a Solution: A telegraph line of length 100 km has a capacity of 0.01 F/km…

A telegraph line of length 100 km has a capacity of 0.01 μ\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 π\pi = 10\sqrt{10} )

Step-by-Step Verified Solution

Total capacitance = 0.01 ×\times 100 = 1 μ\mu F

ω\omega = 500 ×\times 2 π\pi = 1000 π\pi rad/s

ωL=1ωC\omega L = {1 \over {\omega C}}

⇒L=1ω2C=1106π2×10−6=110H\Rightarrow L = {1 \over {{\omega ^2}C}} = {1 \over {{{10}^6}{\pi ^2} \times {{10}^{ - 6}}}} = {1 \over {10}}H = 100 mH

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