A metal rod of the length 10cm and a rectangular cross-section of 1 cm x `1//2` cm is connected to a battery across opposite faces. The resistance will be

Options

A. maximum when the battery is connected across
B. maximum when the battery is connected across
C. maximum when the battery is connected across
D. same irrespective of the three faces.

Answer

To find the resistance of the metal rod, we will use the formula for resistance:

\[ R = \frac{\rho L}{A} \]

where:
- \( R \) is the resistance,
- \( \rho \) is the resistivity of the material,
- \( L \) is the length of the rod,
- \( A \) is the cross-sectional area.

### Step 1: Identify the dimensions of the rod
The length of the rod is given as \( L = 10 \, \text{cm} = 0.1 \, \text{m} \).

The cross-section of the rod is rectangular with dimensions \( 1 \, \text{cm} \times \frac{1}{2} \, \text{cm} \).

### Step 2: Calculate the cross-sectional area
The cross-sectional area \( A \) can be calculated as:

\[ A = \text{width} \times \text{height} = 1 \, \text{cm} \times \frac{1}{2} \, \text{cm} = \frac{1}{2} \, \text{cm}^2 = \frac{1}{2} \times 10^{-4} \, \text{m}^2 = 5 \times 10^{-5} \, \text{m}^2 \]

### Step 3: Substitute values into the resistance formula
Now, substituting the values into the resistance formula:

\[ R = \frac{\rho L}{A} = \frac{\rho \times 0.1 \, \text{m}}{5 \times 10^{-5} \, \text{m}^2} \]

### Step 4: Simplify the expression
This simplifies to:

\[ R = \frac{0.1 \rho}{5 \times 10^{-5}} = \frac{0.1 \rho}{5 \times 10^{-5}} = 2000 \rho \]

### Step 5: Conclusion
The resistance of the metal rod is:

\[ R = 2000 \rho \, \text{ohms} \]