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QJEEM22Ph1261: JEE Main 2022 Physics - Class 12 JEEM22Ph1261 Solution: The length of a given cylindrical wire is increased to double…

The length of a given cylindrical wire is increased to double of its original length. The percentage increase in the resistance of the wire will be ____________ %.

Step-by-Step Verified Solution

Volume is constant so on length doubled

Area is halved so

R=ρlAR = \rho {l \over A} and R′=ρ2lA2=4ρlA=4RR' = \rho {{2l} \over {{A \over 2}}} = 4\rho {l \over A} = 4R

So percentage increase will be

R%=4R−RR×100=300%R\% = {{4R - R} \over R} \times 100 = 300\%

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