In the given figure, a battery of emf $E$ is connnected across a conductor $P Q$ of length $'Y'$ and different area of cross-sections having radii $r_{1}$ and $r_{2}\left(r_{2}\,<\,r_{1}\right)$.
Choose the correct option as one moves from $P$ to $Q$ :
JEE MAIN 2021, Diffcult
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Current is constant in conductor
$i=$ constant
Resistance of element $d R=\frac{\rho d x}{\pi r^{2}}$
$d V=i d R=\frac{i \rho d x}{\pi r^{2}}$
$E=\frac{d V}{d x}=\frac{i \rho}{\pi r^{2}}$
$V_{d}=\frac{e E \tau}{m}$
$\therefore V_{d} \propto E$
$\rightarrow E \propto \frac{1}{r^{2}}$
if $r$ decreases, $E$ will increase $: V_{d}$ will increase
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