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(B) 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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Half of the second

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(B) 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 wires are of the same material,$\rho_1 = \rho_2 = \rho$.Let the length and diameter of the second wire be $l_2 = l$ and $d_2 = d$. Then its area is $A_2 = \pi (d/2)^2 = \pi d^2 / 4$.For the first wire,$l_1 = 2l$ and $d_1 = 2d$. Then its area is $A_1 = \pi (2d/2)^2 = \pi d^2$.Comparing the areas,$A_1 = 4 A_2$.Now,the resistance of the first wire is $R_1 = \rho \frac{l_1}{A_1} = \rho \frac{2l}{4 A_2} = \frac{1}{2} \left( \rho \frac{l}{A_2} \right) = \frac{1}{2} R_2$.Thus,the resistance of the first wire is half of the second wire.

Two wires of the same material are given. The first wire is twice as long as the second and has twice the diameter of the second. The resistance of the first will be

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