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Question

(B) The resistance $R$ of a conductor is given by the formula $R = \rho \frac{l}{A}$,where $\rho$ is the resistivity of the material,$l$ is the length

Vedclass · Accepted Answer

$2A$

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(B) The resistance $R$ of a conductor 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 conductor: $R = \rho \frac{l}{A}$.For the second conductor,the length is $2l$,the resistance is $R$,and the material is the same (so $\rho$ remains constant). Let the new area be $A'$.Then,$R = \rho \frac{2l}{A'}$.Equating the two expressions for $R$: $\rho \frac{l}{A} = \rho \frac{2l}{A'}$.Canceling $\rho$ and $l$ from both sides: $\frac{1}{A} = \frac{2}{A'}$.Solving for $A'$,we get $A' = 2A$.

$A$ cylindrical conductor of length $l$ and uniform area of cross-section $A$ has resistance $R$. Another conductor of length $2l$ and resistance $R$ of the same material has area of cross-section:

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