A current I flows through a uniform wire of diameter d when the mean electron drift velocity is v . The same current will flow through a wire of diameter d / 2 made of the same material if the mean drift velocity of the electron is

Question

A current I flows through a uniform wire of diameter d when the mean electron drift velocity is v . The same current will flow through a wire of diameter d / 2 made of the same material if the mean drift velocity of the electron is (A) v/4 (B) v/2 (C) 2v (D) 4v

Tardigrade Admin · Accepted Answer

j=(I/A)=n e vd (4 I/π d2)=n e v ..... (i) (16 I/π d2)=n e v' .......(ii) From equations (i) and (ii) (4 I/16 I)=(v/v') ⇒ v'=4 v

Q. A current $I$ flows through a uniform wire of diameter $d$ when the mean electron drift velocity is $v .$ The same current will flow through a wire of diameter $d /2$ made of the same material if the mean drift velocity of the electron is

v/4

v/2

2v

4v

$j = \frac{I}{A} = n e v_{d}$
$\frac{4 I}{π d ^{2}} = n e v ..... (i)$
$\frac{16 I}{π d ^{2}} = n e v^{'} ....... (ii)$
From equations (i) and (ii) $\frac{4 I}{16 I} = \frac{v}{v ^{'}}$
$\Rightarrow v^{'} = 4 v$

Q. A current I flows through a uniform wire of diameter d when the mean electron drift velocity is v. The same current will flow through a wire of diameter d/2 made of the same material if the mean drift velocity of the electron is

v/4

v/2

2v

4v

j=AI​=nevd​ πd24I​=nev.....(i) πd216I​=nev′.......(ii) From equations (i) and (ii) 16I4I​=v′v​ ⇒v′=4v

Q. A current $I$ flows through a uniform wire of diameter $d$ when the mean electron drift velocity is $v .$ The same current will flow through a wire of diameter $d /2$ made of the same material if the mean drift velocity of the electron is

$j = \frac{I}{A} = n e v_{d}$
$\frac{4 I}{π d ^{2}} = n e v ..... (i)$
$\frac{16 I}{π d ^{2}} = n e v^{'} ....... (ii)$
From equations (i) and (ii) $\frac{4 I}{16 I} = \frac{v}{v ^{'}}$
$\Rightarrow v^{'} = 4 v$