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(B) The resistance $R$ of a wire is given by the formula $R = \rho \frac{l}{A} = \rho \frac{l}{\pi r^2}$,where $\rho$ is the resistivity (specific res

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The resistance will be halved and the specific resistance will remain unchanged

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(B) The resistance $R$ of a wire is given by the formula $R = ho \frac{l}{A} = ho \frac{l}{\pi r^2}$,where $ho$ is the resistivity (specific resistance),$l$ is the length,and $r$ is the radius.From this,we see that $R \propto \frac{l}{r^2}$.Let the initial length be $l_1 = l$ and initial radius be $r_1 = r$. The new length is $l_2 = 2l$ and the new radius is $r_2 = 2r$.The new resistance $R_2$ is given by:$\frac{R_2}{R_1} = \frac{l_2}{l_1} 	imes \left( \frac{r_1}{r_2} ight)^2 = \left( \frac{2l}{l} ight) 	imes \left( \frac{r}{2r} ight)^2 = 2 	imes \left( \frac{1}{2} ight)^2 = 2 	imes \frac{1}{4} = \frac{1}{2}$.Therefore,$R_2 = \frac{R}{2}$.Specific resistance (resistivity) $ho$ is a material property and does not depend on the dimensions (length or radius) of the wire. Thus,it remains unchanged.

The electric resistance of a certain wire of iron is $R$. If its length and radius are both doubled,then

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