Question

Consider a conductor of variable cross section in which current is flowing from cross section ‘1’ to ‘2’. Then which of the following is/are correct?

• A. Current passing through both the cross sections is same
• B. Current through ‘1’ is less than that through ‘2’
• C. Drift velocity of electrons at ‘1’ is less than that at ‘2’
• D. Drift velocity is same at both the cross sections.

Answer 1

Answer: (A), (C)

The correct options are
A Current passing through both the cross sections is same
C Drift velocity of electrons at ‘1’ is less than that at ‘2’

Using the conservation of charge, it is evident that the amount of charge passing through 2 will be same as it is through 1. Hence current passing through 1 and 2 will be same.
Thus option A is correct and B is incorrect.
The relation between current and drift velocity is given by,
$I=neA{v}_d$
Since current $I$, number of electrons per unit volume $n$ and charge on electron remains constant for cross section 1 and 2, only cross sectional area $A$ and drift velocity of electons $\Rightarrow v_d$ changes.
$v_d\propto \frac{1}{A}$
Since area of section 2 is less than that of 1, therefore drift velocity will be higher at section 2 as compared to that at section 1.
Hence option C is correct and D is incorrect.