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The area of c...

Question

The area of cross section of a current carrying conductor is $A_{0}$ and $\frac{A_{0}}{4}$ at section $(1)$ and $(2)$ respectively. If $v_{1}$ and $v_{2}$ are the drift velocity of region $(1)$ and $(2)$ respectively then

A

v_{1} : v_{2} = 1 : 4

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B

v_{1} : v_{2} = 2 : 1

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C

v_{1} : v_{2} = 3 : 2

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D

v_{1} : v_{2} = 1 : 3

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Solution

The correct option is A $v_{1} : v_{2} = 1 : 4$
Current does not depend on area, i.e. it will be equal through both the cross-sections,

$i_{1} = i_{2}$

$n e A_{0} v_{1} = n e \frac{A_{0}}{4} v_{2}$

$\frac{v_{1}}{v_{2}} = \frac{1}{4}$

$v_{1} : v_{2} = 1 : 4$

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