In a wire of cross section radius $r,$ free electrons travel with drift velocity $v$ when a current $I$ flows through the wire. What is the current in another wire of half the radius and of the same material when the drift velocity is $2v$ ?
Medium
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$I_{1}=\operatorname{ne} A_{1} v_{d_{1}} \& I_{2}=\operatorname{ne} A_{2} v_{d_{2}}$
$\frac{I_{2}}{I_{1}}=\frac{A_{2}}{A_{1}} \times \frac{v_{d_{2}}}{v_{d_{1}}}=\frac{1}{4} \times \frac{2 v}{v} \Rightarrow I_{2}=\frac{I}{2}$
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