Question

In a wire of cross-section radius $r$, free electrons travel with drift velocity $v_d,$ when a current $I$ flows through the wire. What is the current in another wire of half the radius and of the same material, when the drift velocity is $2v_d$ ?

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

Answer 1

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

Given that $v_d^{\prime }=2v_d\text{and}{r}^{\prime }=\frac{r}{2}$
We know that $I=neA{v}_d,A=\pi r^2$
Let current in wire of half radius be
$I^{\prime }=ne{A}^{\prime }{v}_d^{\prime },A^{\prime }=\frac{\pi r^2}{4}$
$I^{\prime }=ne\frac{\pi r^2}{4}{v}_d^{\prime }$
$I^{\prime }=ne\frac{\pi r^2}{4}.2v_d$
$I^{\prime }=\frac{I}{2}$.