A drift velocity of free electrons in a conductor is vd, when the current i is flowing in it. If both the radius and current are doubled, the drift velocity will be :

Question

A drift velocity of free electrons in a conductor is vd, when the current i is flowing in it. If both the radius and current are doubled, the drift velocity will be : (A) (vd/8) (B) (vd/4) (C) (vd/2) (D) vd

Tardigrade Admin · Accepted Answer

If the area of cross-section of wire is

A

and the number of free electrons per unit volume is

n

, then in

t

seconds

n A v_{d} t

electrons will pass it.

The electric current is given by

i = n e A v_{d}

\Rightarrow v_{d} = \frac{i}{n e A}

where

v_{d}

is the drift velocity of the electrons.
Given,

r_{1} = r,

L_{1} = i,

r_{2} = 2 r,

i_{2} = 2 i

\frac{v _{d_{1}}}{v _{d_{2}}} = \frac{i _{1}}{i _{2}} \times \frac{r _{2}^{2}}{r _{1}^{2}}

= \frac{i}{2 i} \times \frac{( 2 r ) ^{2}}{( r ) ^{2}} = 2

\Rightarrow v_{d_{2}} = \frac{v _{d_{1}}}{2}

Note : Direction of drift velocity is opposite to direction of electric field.

Q. A drift velocity of free electrons in a conductor is $v_{d}$ , when the current $i$ is flowing in it. If both the radius and current are doubled, the drift velocity will be :

$\frac{v _{d}}{8}$

$\frac{v _{d}}{4}$

$\frac{v _{d}}{2}$

$v_{d}$

Q. A drift velocity of free electrons in a conductor is vd​, when the current i is flowing in it. If both the radius and current are doubled, the drift velocity will be :

8vd​​

4vd​​

2vd​​

vd​

Q. A drift velocity of free electrons in a conductor is $v_{d}$ , when the current $i$ is flowing in it. If both the radius and current are doubled, the drift velocity will be :

$\frac{v _{d}}{8}$

$\frac{v _{d}}{4}$

$\frac{v _{d}}{2}$

$v_{d}$