Question

An electric current flows along an insulated strip $PQ$ 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 $P$ than at $Q$
• B. The strip is narrower at $Q$ than at $P$
• C. The potential gradient along the strip is uniform
• D. The resistance per unit length of the strip is constant

Answer 1

Answer: (A)

The current density at $P$ is higher than at $Q.$ For the same current flowing through the metallic conductor $PQ$, the cross-sectional area at $P$ is narrower than at $Q.$ The resistance per unit length $r$ is given by $r=\frac{\rho }{A}$ where $\rho$ is the resistivity and $A$ is the cross-sectional area of the conductor $PQ.$ Thus, $r$ is inversely proportional to the cross-sectional area $A$ of the conductor.