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(A) The resistance of a wire is given by $R = \rho \frac{L}{A}$,where $A = \frac{\pi d^2}{4}$.Since the volume of the wire remains constant during str

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$d_2^4: d_1^4$

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(A) The resistance of a wire is given by $R = ho \frac{L}{A}$,where $A = \frac{\pi d^2}{4}$.Since the volume of the wire remains constant during stretching,$V = A_1 L_1 = A_2 L_2$,which implies $L_1 d_1^2 = L_2 d_2^2$,or $\frac{L_1}{L_2} = \frac{d_2^2}{d_1^2}$.The ratio of resistances is $\frac{R_1}{R_2} = \frac{L_1}{L_2} 	imes \frac{A_2}{A_1} = \frac{L_1}{L_2} 	imes \frac{d_2^2}{d_1^2}$.Substituting $\frac{L_1}{L_2} = \frac{d_2^2}{d_1^2}$ into the equation,we get $\frac{R_1}{R_2} = \left(\frac{d_2^2}{d_1^2}ight) 	imes \left(\frac{d_2^2}{d_1^2}ight) = \frac{d_2^4}{d_1^4}$.

$A$ conducting wire has length $L_1$ and diameter $d_1$. After stretching,the same wire's length becomes $L_2$ and diameter $d_2$. The ratio of resistance before and after stretching is:

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