In a wire of circular cross-section with radius ‘r’ free electrons travel with a drift velocity v, when a current I flows through the wire. The current in another wire of half the radius and of the same material when the drift velocity is 2v

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In a wire of circular cross-section with radius ‘r’ free electrons travel with a drift velocity v, when a current I flows through the wire. The current in another wire of half the radius and of the same material when the drift velocity is 2v

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$\frac{I}{4}$

$\frac{I}{2}$

answer is C.

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Detailed Solution

For the given wires of same material current flowing through them is

$I_{1} = {neA}_{1} v . . . . . (1)$

$I_{2} = {neA}_{2} (2 v) . . . . . (2)$

As per the given data, $A_{1} = π r^{2}$ and $A_{2} = π {(\frac{r}{2})}^{2}$

using these values in equation (1) and (2)

$I_{1} = {neπr}^{2} v$ and $I_{2} = ne π {(\frac{r}{2})}^{2} (2 v)$

$∴ I_{2} = \frac{I_{1}}{2}$

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