AIIMS 2019 Physics Drift Velocity MCQ Question

To find the drift speed $v_d$ of electrons in the aluminum wire, we use the formula:

$$v_d = \frac{I}{nqA}$$

where $I$ is the current (10 A), $n$ is the number density of charge carriers, $q$ is the charge of an electron (approximately $1.6 \times 10^{-19}$ C), and $A$ is the cross-sectional area of the wire ($4 \times 10^{-6} \, \text{m}^2$).

First, we calculate $n$ using the density of aluminum (2.7 g/cm³), the molecular weight (27 g/mol), and Avogadro's number ($6.022 \times 10^{23}$ atoms/mol):

$$n = \frac{\text{density} \times 1000 \, \text{kg/m}^3}{\text{molecular weight} \times 10^{-3} \, \text{kg/mol}} \times \text{Avogadro's number} = \frac{2.7 \times 1000}{27 \times 10^{-3}} \times 6.022 \times 10^{23} \approx 6.02 \times 10^{28} \, \text{m}^{-3}$$

Substit