Question

A steady current passes through a wire of non-uniform cross-section. The quantities which depend on the Area of cross-section are:

• A. Free electron density
• B. Resistivity
• C. Drift velocity
• D. Charge crossing in a given time interval

Answer 1

Answer: (C)

Drift velocity

The drift velocity of electrons in a conductor is given by,
$V_d$ $=\frac{I}{nAq}$

where, $I$ is the current, $n$ is the number of electrons, $A$ is the area of cross section and $q$ is the charge on charge carrier.

Steady current means a uniform current throughout the conductor. so current $I$ is constant.

Thus, from this expression the Drift velocity increases inversely as area decreases.

So now the Drift velocity is inversely related to area $A$,

such that for larger areas of cross section, $V_d$ is lower and for lower areas of cross section $V_d$ is higher.

$A$$V_d$ is nearly constant such that current $I$ remains same through any cross section of the wire.

The density of free electrons is number of free electrons per unit volume. which only depend upon material of the conductor, it's a constant value for same material because it is calculated over per unit volume.

So it is not affected by $V$ or $A$. Hence Option A is wrong.

Resistivity of a material depends on the material alone and is independent of the length or cross section Area of the wire. Hence, option B is wrong.

Charge crossing in a given time interval is current $I$ itself, which is given constant for any cross section in the wire. Hence option D is wrong.