Question

An electric current flows along an insulated strip $\text{PQ}$ of a metallic conductor. The current density in the strip varies as shown in the graph. Which one of the following statements could explain this variation?

• A. The strip is narrower at $\text{P}$ than at $\text{Q}$
• B. The strip is narrower at $\text{Q}$ than at $\text{P}$
• C. The potential gradient along the strip is uniform
• D. The resistance per unit length of the strip is constant.

Answer 1

The correct option is A The strip is narrower at $\text{P}$ than at $\text{Q}$

The same current flows through the entire strip $\text{PQ}$.

Let the current flowing be current is $i$

So, the current density at any point $J=\frac{i}{A}$

Where, $A$ $=$ Cross-sectional area of strip.

Since, $J$ decreases as we move from $\text{P}$ to $\text{Q}$.

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

Hence, $A$ should increase as we move from $\text{P}$ to $\text{Q}$

$\Rightarrow$ Strip will be narrower at $\text{P}$ end as compared to $\text{Q}$ end.

Why this Question ? Key point : In a current carrying conductor, the current at all points remain same, However, the current density varies depending upon the cross-sectional area.