NEET Basics of Current MCQs & PYQs

In a conductor, free electrons are in constant random thermal motion. Due to this random orientation, for every electron moving in one direction, there's another moving in a roughly opposite direction, leading to a cancellation of their velocities. Therefore, the vector sum of these random velocities, which is the average thermal velocity, is zero. Both (A) and (R) are true, and (R) correctly explains (A).

Assertion (A) is true: The thermal motion of electrons is random, so their average velocity vector \( langle vec{v}_{th} rangle \) is zero. Reason (R) is false: Electrons in a conductor are in continuous, random thermal motion even in the absence of an external electric field; they are not at rest.

For a semiconductor, resistivity actually \(\text{decreases}\) with increasing temperature because more charge carriers (electrons and holes) are generated. The reason given describes the behavior of conductors, where increased atomic vibrations impede electron flow, increasing resistivity. Thus, both Assertion (A) and Reason (R) are false for a semiconductor.

Assertion (A) is true: Copper is widely used for connecting wires due to its excellent electrical conductivity and ductility. Reason (R) is false: Copper is a good conductor but not a superconductor at room temperature; it exhibits electrical resistance. Superconductivity typically occurs at very low temperatures for specific materials.

Assertion (A) is false because current is a scalar quantity and its addition follows Kirchhoff's current law (algebraic sum), not vector addition. Reason (R) is false because while current is a scalar, it does not add like a vector; it adds algebraically.

If an observer moves with the electron drift speed (in the direction of electron flow), electrons are at rest relative to them. However, the positive lattice ions, which were stationary in the conductor's frame, are now moving. This motion of positive ions constitutes a current and produces a magnetic field.

Thus, (A) is false. Also, in this frame, only electrons are at rest, while positive ions are moving, so (R) is false.

Using \(R = \rho \frac{l}{A} = \rho \frac{l}{\pi (d/2)^2} \propto \frac{1}{d^2}\). Since diameter \(d_B = 3d_A\), the resistance \(R_B = \frac{R_A}{3^2} = \frac{81}{9} = 9 \Omega\).

Using \(I = n e A v_d ⇒ v_d = \frac{I}{n e \pi r^2}\). Substituting values, we get \(v_d = \frac{10}{10^{22} \times 1.6 \times 10^{-19} \times \pi \times (10^{-3})^2} = \frac{6.25}{\pi} \times 10^3 \text{ms}^{-1}\).

Copper ($\text{Cu}$), Silver ($\text{Ag}$), and Gold ($\text{Au}$) are all metals with high free-electron density, making them excellent conductors of electricity.