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(C) The drift velocity $v_d$ of electrons in a conductor is given by the formula $v_d = \frac{I}{neA}$,where $I$ is the current,$n$ is the number dens

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$v_P = \frac{1}{4}v_Q$

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(C) The drift velocity $v_d$ of electrons in a conductor is given by the formula $v_d = \frac{I}{neA}$,where $I$ is the current,$n$ is the number density of electrons,$e$ is the charge of an electron,and $A$ is the cross-sectional area.Since $I$,$n$,and $e$ are constant for both sections,we have $v_d \propto \frac{1}{A}$.The area of cross-section $A$ is given by $A = \pi r^2 = \pi (d/2)^2 = \frac{\pi d^2}{4}$,which implies $A \propto d^2$.Therefore,$v_d \propto \frac{1}{d^2}$.For sections $P$ and $Q$,we have $\frac{v_P}{v_Q} = \left( \frac{d_Q}{d_P} \right)^2$.Given $d_P = d$ and $d_Q = d/2$,we get $\frac{v_P}{v_Q} = \left( \frac{d/2}{d} \right)^2 = \left( \frac{1}{2} \right)^2 = \frac{1}{4}$.Thus,$v_P = \frac{1}{4}v_Q$.

$A$ current $I$ is passing through a wire having two sections $P$ and $Q$ of uniform diameters $d$ and $d/2$ respectively. If the mean drift velocity of electrons in sections $P$ and $Q$ is denoted by $v_P$ and $v_Q$ respectively,then

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