Question

A wire has a non-uniform cross-section, as shown in the figure. A steady current flows through it. The drift speed of electrons at points $P$ and $Q$ are $v_P$ and $v_Q$ respectively, then -

• A. $v_P=v_Q$
• B. $v_P<v_Q$
• C. $v_P>v_Q$
• D. Data insufficient

Answer 1

The correct option is C $v_P>v_Q$

We know that,
$$i=neA{v}_d$$
where,
$i\to$ current
$n\to$ number of free electrons per unit volume
$e\to$ charge of an electron
$A\to$ cross-sectional area
$v_d\to$ drift speed

For steady current, $v_d\propto \frac{1}{A}$

From figure,

$A_P<A_Q\Rightarrow v_P>v_Q$

Key Concept: If current is constant, then as cross-sectional area of conductor increases, the drift velocity decreases.