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 in the figure.


Which 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 $\text{Q}$.

From definition of current density $J$,

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

For constant current,

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

Here, the current density at $\text{P}$ is higher than that at $\text{Q}$.

For the same current flowing through the metallic conductor $\text{PQ}$, the cross-sectional area at $\text{P}$ is narrower than that strip $\text{Q}$.

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