Question

A metal rod of length 10 cm and a rectangular cross section of 1 cm $\times$ 1/2 cm is connected to a battery across opposite faces. The resistance will be _____.

• A. Maximum when the battery is connected across 1 cm $\times$ 1/2 cm faces.
• B. Maximum when the battery is connected across 10 cm $\times$ 1/2 cm faces.
• C. Maximum when the battery is connected across 10 cm $\times$ 1 cm faces.
• D. Same irrespective of the three faces.

Hint:

To get \textbf{Maximum Resistance}, push current through the "Longest and Thinnest" path. To get \textbf{Minimum Resistance}, use the "Shortest and Widest" path.

Answer 1

The Correct Option is A

Step 1: Understanding the Concept:
Resistance is defined by the formula $R = \rho \frac{L}{A}$, where $\rho$ is resistivity, $L$ is the length along the path of current, and $A$ is the area of the face through which current enters.
Step 2: Detailed Explanation:
To maximize $R$, we need to maximize $L$ and minimize $A$.

• If connected across $1\text{ cm} \times 1/2\text{ cm}$ faces, the length $L = 10\text{ cm}$ (the longest dimension) and $A = 0.5\text{ cm}^2$ (the smallest area).
• In any other configuration, the path length $L$ would be shorter ($1\text{ cm}$ or $0.5\text{ cm}$) and the area $A$ would be larger.

Thus, the resistance is maximum when the current travels the longest path through the smallest cross-section.
Step 3: Final Answer:
The resistance is maximum in case (a).