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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 of the material,$l$ is the length,and

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$R/4$

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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 of the material,$l$ is the length,and $a$ is the area of cross-section.For the first wire: $R = \rho \frac{l}{a}$.For the second wire,the material is the same (so $\rho$ is constant),the length is the same $(l)$,and the area of cross-section is $4a$.Therefore,the new resistance $R'$ is given by $R' = \rho \frac{l}{4a}$.Substituting the expression for $R$,we get $R' = \frac{1}{4} \left( \rho \frac{l}{a} \right) = \frac{R}{4}$.

An electric wire of length $l$ and area of cross-section $a$ has a resistance $R \ \Omega$. Another wire of the same material having the same length and area of cross-section $4a$ has a resistance of:

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