Two wires A an dB of the same material, having radii in the ratio I : 2 and carry currents in the ratio 4: I. The ratio of drift speed of electrons in A and Bis :

Options

A. `16:1`
B. `1:16`
C. `1:4`
D. `4:1 `

Answer

A

Explanation

Drift speed of electrons is given by
`I = n e A v _(d),` where
n, e, `A & v _(d)` represents electron number density, charge of electron. crosssectional area and drift velocity respectively.
Therefore ` v _(d) prop ( I )/( r ^(2))`
`((v _(d)) _(A))/( ( v _(d)) _(B)) = ( I _(A))/( I _(B)) xx ( r_(B) ^(2))/( r _(A) ^(2))`
`(( v _(d))_(A))/( ( v _(d)) _(B))= (4)/(1) xx (2 ^(2))/(1 ^(2)) = (16)/(1)`