Question

A wire has a nonuniform cross sectional area as shown in the figure. A steady current i flows through it. Which one of the following statements is correct?

• A. Drift speed of the electrons is constant
• B. Drift speed of decreases on moving from A to B
• C. Drift speed of increases on moving from A to B
• D. Drift speed varies randomly

Answer 1

The correct option is B Drift speed of decreases on moving from A to B

The current through the conductor is given by

$i=neA{v}_d$

where, n is number of electrons crossing per unit area, e is electronic charge, A is area of cross section of conductor and $v_d$ is the drift velocity(speed) of electrons.

We can write from above equation

$v_d=\frac{i}{neA}$

Since, a steady(constant) current i flows through the given conductor and n and e are constant, hence drift speed is inversely proportional to the area of cross section of conductor i.e.

$v_d\propto \frac{1}{A}$

As the area of cross section of given conductor is increases from A to B, hence drift speed of electrons decreases on moving from A to B