JEE Main 2022PhysicsAlternating CurrentMediumNumerical

JEE Main 2022 — Alternating Current Question with Solution

JEE Main 2022 (28 Jun Shift 1)

Question

A telegraph line of length 100 km has a capacity of 0.01 μF 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)

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Show full solutionCorrect answer: 100
Correct answer
100

Step-by-step explanation

The frequency given is 0.5 kilo cycle per second ⇒f=500 Hz⇒ω=2πf=1000π 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

XL=XC

⇒ωL=1ωC⇒L=1ω2C=110002×π2×0.01×10-6×100=10-1 H=100 mH

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About this question

This is a previous-year question from JEE Main 2022, covering the Alternating Current chapter of Physics. PrepSharp catalogues every PYQ from JEE Main with a verified answer key and step-by-step solution prepared by IIT alumni — so you can search by chapter, topic or year and revise efficiently.