A wire
Question:

A wire of $1 \Omega$ has a length of $1 \mathrm{~m}$. It is stretched till its length increases by $25 \%$. The percentage change in a resistance to the nearest integer is:

  1. (1) $25 \%$

  2. (2) $12.5 \%$

  3. (3) $76 \%$

  4. (4) $56 \%$


Correct Option: , 4

Solution:

(4)

For stretched or compressed wire

$\mathrm{R} \propto \mathrm{I}^{2}$

$\frac{R_{1}}{R_{2}}=\frac{l_{1}^{2}}{l_{2}^{2}}$

$\Rightarrow \frac{\mathrm{R}}{\mathrm{R}_{2}}=\frac{\mathrm{R}^{2}}{(1.251)^{2}}$

$\Rightarrow \mathrm{R}_{2}=1.5625 \mathrm{R}$

$\%$ increase $\rightarrow 56.235 \%$

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