PYQ NEET- Current Electricity L-2

Question: A copper wire of radius $1 \mathrm{~mm}$ contains $10^{22}$ free electrons per cubic metre. The drift velocity for free electrons when $10 \mathrm{~A}$ current flows through the wire will be (Given, charge on electron $=1.6 \times 10^{-19} \mathrm{C}$ ) : (2023)#

A) $\frac{6.25 \times 10^4}{\pi} \mathrm{ms}^{-1}$

B) $\frac{6.25}{\pi} \times 10^3 \mathrm{~ms}^{-1}$

C) $\frac{6.25}{\pi} \mathrm{ms}^{-1}$

D) $\frac{6.25 \times 10^5}{\pi} \mathrm{ms}^{-1}$

Answer: $\frac{6.25}{\pi} \times 10^3 \mathrm{~ms}^{-1}$#

Explanation#

$\begin{aligned} & \mathrm{I}=\mathrm{neAV}{\mathrm{d}} \ & \mathrm{V}{\mathrm{d}}=\frac{\mathrm{I}}{\mathrm{neA}}=\frac{10}{10^{22} \times 1.6 \times 10^{-19} \times \pi \times 10^{-6}} \ & \mathrm{~V}_{\mathrm{d}}=\frac{6.25}{\pi} \times 10^3 \mathrm{~m} / \mathrm{sec}\end{aligned}$