NEET Practice Questions (MCQs) with Answers & Solutions

From the NCERT text, the average velocity $v_d$ is given by $v_d = -\frac{eE\tau}{m}$. This is derived from averaging the acceleration experienced by electrons between collisions. (NCERT, Eq. 3.17, page 86)

The amount of charge crossing area A in time $\Delta t$ is $I\Delta t$. This is also equal to $neA|v_d|\Delta t$. Therefore, $I = neA|v_d|$. (NCERT, Eq. 3.18, page 86)

The relaxation time ($\tau$) is defined as the average time between successive collisions of an electron with the positive ions in the conductor. The NCERT text states, 'The average value of $t_i$ then is $\tau$ (known as relaxation time).' (NCERT, page 86)

Each 'free' electron does accelerate, increasing its drift speed until it collides with a positive ion of the metal. It loses its drift speed after collision but starts to accelerate and increases its drift speed again only to suffer a collision again and so on. On the average, therefore, electrons acquire only a drift speed. (NCERT, Example 3.2 (b), page 88)

The drift speed of electrons is much smaller, about $10^{-5}$ times the typical thermal speed at ordinary temperatures. Thermal speeds are typically of the order of $2 \times 10^2$ m/s, while drift speeds are around $1.1 \times 10^{-3}$ m/s. (NCERT, Example 3.1 (b) (i), page 87-88)

Electric field is established throughout the circuit, almost instantly (with the speed of light) causing at every point a local electron drift. Establishment of a current does not have to wait for electrons from one end of the conductor traveling to the other end. (NCERT, Example 3.2 (a), page 88)

The current density $j$ gives the amount of charge flowing per second per unit area normal to the flow, and is related to drift velocity by $j = nq v_d$. For electrons, $q = -e$, so the magnitude is $|j| = n e v_d$. (NCERT, Point 7 in Summary, page 103)

Simple, because the electron number density is enormous, $\sim 10^{29} \text{ m}^{-3}$. A vast number of charge carriers, even moving slowly, can transport significant charge. (NCERT, Example 3.2 (c), page 88)

In the absence of an electric field, the paths are straight lines; in the presence of an electric field, the paths are, in general, curved. This is due to the acceleration caused by the electric field between collisions. (NCERT, Example 3.2 (e), page 88)

Comparing the vector form of Ohm's law, $\vec{j} = \sigma \vec{E}$ (Eq. 3.13), with the derived equation $\vec{j} = \frac{ne^2\tau}{m} \vec{E}$ (Eq. 3.22), we find that $\sigma = \frac{ne^2\tau}{m}$ (Eq. 3.23). (NCERT, Eq. 3.22 and 3.23, page 86-87)