A uniform wire of diameter carries a current of 100 mA when the mean drift velocity of electrons in the wire is . For a wire of diameter of the same material to carry a current of 200 mA, the mean drift velocity of electrons in the wire is [

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Solution

Q.
A uniform wire of diameter $d$ carries a current of 100 mA when the mean drift velocity of electrons in the wire is $v$ . For a wire of diameter $\frac{d}{2}$ of the same material to carry a current of 200 mA, the mean drift velocity of electrons in the wire is [2024]

1 $4 v$

2 $8 v$

3 $v$

4 $2 v$

Ans.
(2)

As we know, $I = n A e v_{d}$

where, $I = 100 mA,$ diameter $= d$ and $v_{d} = v$

$100$ $mA = n A e v$ ...(i)

Now, $I = 200$ $mA$ , diameter $= \frac{d}{2}$ and $v_{d} = v'$

$200$ $mA = n A' e v'$ ...(ii)

From equations (i) and (ii),

$\frac{100}{200} = \frac{n A e v}{n A' e v'}; \frac{1}{2} = \frac{π \times d^{2} / 4 \times v}{π \times d^{2} / 16 \times v'}$ $;$ $\frac{1}{2} = \frac{4 v}{v'} \Rightarrow v' = 8 v$

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