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(B) The drift velocity $v_{d}$ is given by the formula $v_{d} = \frac{I}{neA}$.Since $I = \frac{V}{R}$ and $R = \frac{\rho \ell}{A}$,we substitute the

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$\frac{V_d}{2}$

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(B) The drift velocity $v_{d}$ is given by the formula $v_{d} = \frac{I}{neA}$.Since $I = \frac{V}{R}$ and $R = \frac{\rho \ell}{A}$,we substitute these into the equation:$v_{d} = \frac{V}{neAR} = \frac{V}{neA (\frac{\rho \ell}{A})} = \frac{V}{ne \rho \ell}$.Here,$V$ is the potential difference,$n$ is the electron density,$e$ is the charge of an electron,$\rho$ is the resistivity,and $\ell$ is the length of the wire.From the formula,we see that $v_{d} \propto \frac{1}{\ell}$.If the length $\ell$ is doubled $(\ell' = 2\ell)$,the new drift velocity $v_{d}'$ becomes:$v_{d}' = \frac{V}{ne \rho (2\ell)} = \frac{1}{2} \left( \frac{V}{ne \rho \ell} \right) = \frac{V_{d}}{2}$.Note that the area of cross-section $A$ cancels out in the expression for drift velocity when the potential difference $V$ is kept constant.

The drift velocity of electrons in a conducting wire connected to a cell is $V_{d}$. If the length of the wire is doubled and the area of cross-section is halved,then the drift velocity of electrons becomes:

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