Dimensions of a block are `1 cm xx 1cm xx 100cm`. If specific resistance of its material is `3 xx 10^(-7) ohm-m`, then the resistance between the opposite rectangular facesis

Options

A. `3 xx 10^(-9) ohm`
B. `3 xx 10^(-7) ohm`
C. `3 xx 10^(-5) ohm`
D. `3 xx 10^(-3) ohm`

Answer

To find the resistance between the opposite rectangular faces of the block, we can use the formula for resistance:

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

Where:
- \( R \) is the resistance,
- \( \rho \) is the specific resistance (resistivity) of the material,
- \( L \) is the length of the conductor through which the current flows,
- \( A \) is the cross-sectional area of the conductor.

### Step-by-Step Solution

1. **Identify the dimensions of the block**:
- The dimensions of the block are given as \( 1 \, \text{cm} \times 1 \, \text{cm} \times 100 \, \text{cm} \).
- We need to find the resistance between the opposite rectangular faces, which means we will take the length \( L \) as \( 100 \, \text{cm} \) (the longest side).

2. **Convert dimensions to meters**:
- Convert \( L \) from centimeters to meters:
\[ L = 100 \, \text{cm} = 1 \, \text{m} \]
- Convert the cross-sectional dimensions from centimeters to meters:
\[ \text{Cross-sectional area} = 1 \, \text{cm} \times 1 \, \text{cm} = 1 \, \text{cm}^2 = 1 \times 10^{-4} \, \text{m}^2 \]

3. **Substitute the values into the resistance formula**:
- Given specific resistance \( \rho = 3 \times 10^{-7} \, \Omega \cdot \text{m} \),
- Substitute \( \rho \), \( L \), and \( A \) into the formula:
\[ R = \frac{(3 \times 10^{-7} \, \Omega \cdot \text{m}) \times (1 \, \text{m})}{(1 \times 10^{-4} \, \text{m}^2)} \]

4. **Calculate the resistance**:
- Performing the calculation:
\[ R = \frac{3 \times 10^{-7}}{1 \times 10^{-4}} = 3 \times 10^{-3} \, \Omega \]

5. **Final answer**:
- The resistance between the opposite rectangular faces is:
\[ R = 3 \, \text{m}\Omega \]