Question

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

• A. $\frac{{{v}_{d}}}{8}$
• B. $\frac{{{v}_{d}}}{4}$
• C. $\frac{{{v}_{d}}}{2}$
• D. ${{v}_{d}}$

Answer 1

Answer: (C)

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

Answer 2

$i=neA{{v}_{d}}$ ${{v}_{d}}=\frac{i}{neA}$ where, ${{v}_{d}}$ is the drift velociy-of the electron $\frac{{{v}_{{{d}_{1}}}}}{{{v}_{{{d}_{2}}}}}=\frac{{{i}_{1}}}{{{i}_{2}}}\times \frac{r_{2}^{2}}{r_{1}^{2}}$ $=\frac{i}{2i}\times \frac{2{{n}^{2}}}{{{n}^{2}}}=2$ ${{v}_{{{d}_{2}}}}=\frac{{{v}_{{{d}_{1}}}}}{2}=\frac{{{v}_{d}}}{2}$