The resistance of a metal rod of length 10 cm and rectangular cross-section of `1 cm xx (1)/(2)` connected to a battery across opposite faces is maximum when the battery is connected across.

Options

A. `10 cm xx (1)/(2) ` cm faces
B. `1 cm xx (1)/(2) cm` cm faces
C. `10 cm xx 1` cm faces
D. `10 cm xx (1)/(2) cm ^(2)` faces

Explanation

To solve the problem, we need to determine the configuration that maximizes the resistance of the metal rod when connected to a battery.

### Step 1: Understand the formula for resistance
The resistance \( R \) of a conductor is given by the formula:
\[ R = \frac{\rho L}{A} \]
where:
- \( R \) is the resistance,
- \( \rho \) is the resistivity of the material,
- \( L \) is the length of the conductor,
- \( A \) is the cross-sectional area.

### Step 2: Identify the dimensions of the rod
The rod has a length \( L = 10 \, \text{cm} \) and a rectangular cross-section of \( 1 \, \text{cm} \times \frac{1}{2} \, \text{cm} \).

### Step 3: Calculate the cross-sectional area
The cross-sectional area \( A \) can be calculated as:
\[ A = \text{width} \times \text{height} = 1 \, \text{cm} \times \frac{1}{2} \, \text{cm} = \frac{1}{2} \, \text{cm}^2 \]

### Step 4: Analyze the resistance
From the resistance formula, we see that:
- Resistance \( R \) is directly proportional to the length \( L \) of the rod.
- Resistance \( R \) is inversely proportional to the cross-sectional area \( A \).

### Step 5: Determine maximum resistance configuration
To maximize the resistance:
- We want the length \( L \) to be as long as possible (which is already given as 10 cm).
- We want the cross-sectional area \( A \) to be as small as possible.

### Step 6: Conclusion
Since the cross-sectional area is fixed at \( \frac{1}{2} \, \text{cm}^2 \), the maximum resistance occurs when the battery is connected across the length of the rod. Therefore, the configuration that maximizes resistance is when the battery is connected across the longer dimension of the rod.

### Final Answer
The resistance of the metal rod is maximum when the battery is connected across the length of the rod.

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