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 $R$ of a conductor is given by $R = \rho \frac{L}{A}$, where $\rho$ is resistivity, $L$ is the length along the direction of current, and $A$ is the area of the cross-section perpendicular to the current.
Step 2: Formula Application:
To make $R$ maximum, we need the largest possible $L$ and the smallest possible $A$. The dimensions are 10 cm, 1 cm, and 0.5 cm. The maximum possible length is $L = 10$ cm.
Step 3: Explanation:
When $L = 10$ cm, the faces perpendicular to the current are the $1$ cm $\times$ $0.5$ cm faces. This gives the smallest area $A = 0.5$ cm$^2$. Since $L$ is maximum and $A$ is minimum, the resistance is maximized.
Step 4: Final Answer:
The resistance is maximum when connected across the 1 cm $\times$ 1/2 cm faces.