Question

A wire has a non-uniform cross-section as shown in figure. A steady current flows through it. The drift speed of electrons at point $\text{P}$ and $\text{Q}$ is $v_P$ and $v_Q$.

• 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 from current -drift velocity relation

$I=neA{v}_d$

As the cross-section are in series, so the current in them will be the same. And $n\&e$ are also same. So we get

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

At one cross-section is more, hence the drift velocity is less.
Here,
$A_P<A_Q$

$\therefore v_P>v_Q$

Hence, $\left(c\right)$ is correct option.

Why This Question? If current is constant then as area of conductor increases then drift velocity decreases. Current density can be represented by a similar set of lines known as streamlines. The spacing of the streamlines suggests the value of current density. Narrower streamlines mean more current density, spaced streamlines mean less current density