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 d/2 of the same material to carry a current of 200 mA, the mean drift velocity of electrons in the wire is (a) 4v (b) 8v (c) v (d) 2v

Answer: (b). vd = I/neA ∝ Id² for the same material v'/v = (200)/(100) × (d/d/2)² = 2 × 4 = 8 So the answer is (b) 8v.

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Q7NEET 2024Medium

Electric Current, Drift Velocity & Current Density

A uniform wire of diameter $d$ carries a current of $100\text{ mA}$ 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 $200\text{ mA}$ , the mean drift velocity of electrons in the wire is

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Answer: (b)

$v_d = \dfrac{I}{neA} \propto \dfrac{I}{d^{2}}$ for the same material
$\dfrac{v'}{v} = \dfrac{200}{100} \times \left(\dfrac{d}{d/2}\right)^{2} = 2 \times 4 = 8$
So the answer is (b) $8v$ .

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