Question

In a wire of circular cross-section with radius r, free electrons travel with a drift velocity v, when a current i flows through the wire. What is the current in another wire of half the radius and of the some material when the drift velocity is 2v

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

Answer 1

The correct option is C $\frac{i}{2}$

$i=neA{v}_d=ne\pi r^{2}v$ and $i_1=ne\pi {\left(\frac{r}{2}\right)}^2.2v=\frac{ne\pi r^{2}v}{2}=\frac{i}{2}$