The resistance of a wire is $R$. It is bent at the middle by $180^o$ and both the ends are twisted together to make a shorter wire. The resistance of the new wire is
AIEEE 2012, Medium
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Resistance of wire $(R)=\rho \frac{1}{A}$
If wire is bent in the middle then
$l'=\frac{1}{2}, A^{\prime}=2\, A$
$\therefore $ $\text { New resistance, } \mathrm{R}^{\prime} =\rho \frac{l^{\prime}}{\mathrm{A}^{\prime}} $
$=\frac{\rho \frac{l}{2}}{2\, A}=\frac{\rho l}{4\, A}=\frac{R}{4}$
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