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)Omega`
B. `3 xx 10^(-7)Omega`
C. `3 xx 10^(-5)Omega`
D. `3 xx 10^(-3)Omega`

Answer

To find the resistance between the opposite rectangular faces of the block, we can follow these steps:

### Step 1: Identify the dimensions of the block
The dimensions of the block are given as:
- Length (L) = 1 cm
- Width (W) = 1 cm
- Height (H) = 100 cm

### Step 2: Determine the area of the cross-section
The area (A) of the rectangular face through which the current flows is given by:
\[ A = \text{Width} \times \text{Height} = 1 \, \text{cm} \times 100 \, \text{cm} = 100 \, \text{cm}^2 \]

### Step 3: Convert units to meters
Since the specific resistance (resistivity) is given in ohm-meters, we need to convert the dimensions from centimeters to meters:
- 1 cm = 0.01 m
- Therefore, the area in square meters is:
\[ A = 100 \, \text{cm}^2 = 100 \times (0.01 \, \text{m})^2 = 100 \times 0.0001 \, \text{m}^2 = 0.01 \, \text{m}^2 \]

### Step 4: Identify the specific resistance
The specific resistance (ρ) of the material is given as:
\[ \rho = 3 \times 10^{-7} \, \text{ohm-m} \]

### Step 5: Calculate the resistance using the formula
The resistance (R) between the opposite rectangular faces can be calculated using the formula:
\[ R = \frac{\rho \cdot L}{A} \]
Where:
- L = Length of the block (the distance between the two faces) = 1 cm = 0.01 m
- A = Area of cross-section = 0.01 m²

Substituting the values:
\[ R = \frac{(3 \times 10^{-7} \, \text{ohm-m}) \cdot (0.01 \, \text{m})}{0.01 \, \text{m}^2} \]

### Step 6: Simplify the equation
\[ R = \frac{3 \times 10^{-7} \cdot 0.01}{0.01} \]
\[ R = 3 \times 10^{-7} \, \text{ohm} \]

### Final Answer
The resistance between the opposite rectangular faces is:
\[ R = 3 \times 10^{-7} \, \text{ohm} \]

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