Question

A current passes through a wire of nonuniform cross-section. Which of the following quantities is independent of the cross-section?

• A. The charge crossing in a given time interval.
• B. Drift speed
• C. Current density
• D. None of these

Answer 1

The correct option is A The charge crossing in a given time interval.

Since,
Charge entering at one end of a conductor = charge leaving at the other end,

So current does not change with change in cross-section and conductor remains uncharged when current flows through it.

As the cross-sections are in series, so the current in them will be the same.

From current and drift velocity relation,

$I=neA{v}_d$

Since, in this case current and $n$ are constant

$\therefore v_d\propto 1/A$.

At one cross-section is more, hence the drift velocity is less.

And current density $J$ is given by

$J=\frac{I}{A}$

$\Rightarrow J\propto \frac{1}{A}(\because I=\text{constant})$

So, current density depends upon area of cross-section.

Hence, option $\left(a\right)$ is correct