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(A) The resistance $R$ of a wire is given by the formula $R = \rho \frac{L}{A}$,where $\rho$ is the resistivity,$L$ is the length,and $A$ is the cross

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The resistance will be halved and the resistivity will remain unchanged.

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(A) The resistance $R$ of a wire is given by the formula $R = \rho \frac{L}{A}$,where $\rho$ is the resistivity,$L$ is the length,and $A$ is the cross-sectional area.Since the wire is cylindrical,the area $A = \pi r^2$,where $r$ is the radius.Therefore,$R = \rho \frac{L}{\pi r^2}$.When the length $L$ is doubled $(L' = 2L)$ and the radius $r$ is doubled $(r' = 2r)$,the new resistance $R'$ is:$R' = \rho \frac{2L}{\pi (2r)^2} = \rho \frac{2L}{\pi (4r^2)} = \frac{1}{2} \left( \rho \frac{L}{\pi r^2} \right) = \frac{R}{2}$.Resistivity $(\rho)$ is a material property that depends only on the nature of the material and temperature,not on the dimensions of the wire. Thus,it remains unchanged.Therefore,the resistance is halved and the resistivity remains unchanged.

The electrical resistance of an iron wire is $R$. If both its length and radius are doubled,then:

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