Question

A copper wire is connected across an ideal battery. The drift velocity of the electrons is $v$. If another copper wire of the same length and double the radius is connected across the same battery, the drift velocity will be:

• A. $v$
• B. $2v$
• C. $\frac{v}{4}$
• D. $4v$

Answer 1

The correct option is C $\frac{v}{4}$

We know that

$J=\frac{I}{A}=nevv=\frac{I}{neA}$

$A=\pi r^2$

If radius will be double than

$A=\pi {\left(2r\right)}^2=4\pi r^2$

Then drift velocity will become

$v=\frac{I}{ne\left(4\pi r^2\right)}=\frac{v}{4}$

Hence, option(c) is correct option