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