QJEEM23Ph4f70: JEE Main 2023 Physics - Class 12 JEEM23Ph4f70 Solution: If a copper wire is stretched to increase its length by 20%.…

Question

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If a copper wire is stretched to increase its length by 20%. The percentage increase in resistance of the wire is __________%.

Accepted Answer

Let

\ell_{0}

be its initial length and

A_{0}

be initial area.

Considering volume to be conserved

\begin{aligned} Vol. = ℓ_{0} A_{0} = (1.2 ℓ_{0}) A \\ A_{final} = \frac{A_{0}}{1.2} \\ R_{in} = \frac{ρ ℓ_{0}}{A_{0}} \\ R_{final} = \frac{ρ 1.2 ℓ_{0}}{\frac{A_{0}}{1.2}} = \frac{ρ ℓ_{0}}{A_{0}} (1.2)^{2} \end{aligned}

=\mathrm{R}_{\text {in }}(1.44)

Hence increase

=44 \%

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