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

Options

A. maximum when the battery is connected across `1cmxx(1)/(2)cm` faces
B. maximum when the battery is connected across `10cmxx1cm` faces
C. maximum when the battery is connected across `10cmxx(1)/2 cm` faces.
D. Same irrespective of the three faces.

Explanation

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 (which is a constant for a given material),
- \( L \) is the length of the rod,
- \( A \) is the cross-sectional area.

### Step 1: Identify the dimensions of the rod
The length \( L \) of the rod is given as 10 cm. We need to convert this to meters for standard SI units:

\[ L = 10 \, \text{cm} = 0.1 \, \text{m} \]

### Step 2: Calculate the cross-sectional area \( A \)
The cross-section of the rod is given as \( 1 \, \text{cm} \times \frac{1}{2} \, \text{cm} \). We convert these dimensions to meters:

\[ 1 \, \text{cm} = 0.01 \, \text{m} \]
\[ \frac{1}{2} \, \text{cm} = 0.005 \, \text{m} \]

Now we can calculate the area \( A \):

\[ A = 0.01 \, \text{m} \times 0.005 \, \text{m} = 0.00005 \, \text{m}^2 \]

### Step 3: Substitute values into the resistance formula
Now we can substitute \( L \) and \( A \) into the resistance formula. We will need the resistivity \( \rho \) of the material, which is not provided in the question. For this example, let’s assume the resistivity \( \rho \) is a known constant (e.g., for copper, \( \rho \approx 1.68 \times 10^{-8} \, \Omega \cdot m \)).

\[ R = \frac{\rho \cdot 0.1}{0.00005} \]

### Step 4: Calculate the resistance
Substituting the value of \( \rho \):

\[ R = \frac{1.68 \times 10^{-8} \cdot 0.1}{0.00005} \]
\[ R = \frac{1.68 \times 10^{-9}}{0.00005} = 3.36 \times 10^{-5} \, \Omega \]

### Conclusion
The resistance of the metal rod is \( R = 3.36 \times 10^{-5} \, \Omega \) (assuming the resistivity of the material is known).