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 square faces is

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 square faces of a cuboid with given dimensions and specific resistance, we will follow these steps:

### Step 1: Identify the dimensions and specific resistance
The dimensions of the block are:
- Length (L) = 100 cm
- Breadth (B) = 1 cm
- Height (H) = 1 cm

The specific resistance (ρ) of the material is given as:
- ρ = \(3 \times 10^{-7}\) ohm-m

### Step 2: Convert dimensions to meters
Since the specific resistance is given in ohm-meters, we need to convert the dimensions from centimeters to meters:
- Length (L) = 100 cm = \(100 / 100 = 1\) m
- Breadth (B) = 1 cm = \(1 / 100 = 0.01\) m
- Height (H) = 1 cm = \(1 / 100 = 0.01\) m

### Step 3: Calculate the area of cross-section (A)
The area of cross-section (A) is the area of the square face:
- A = Breadth × Height = \(0.01 \, \text{m} \times 0.01 \, \text{m} = 0.0001 \, \text{m}^2\)

### Step 4: Use the formula for resistance
The resistance (R) between the opposite square faces can be calculated using the formula:
\[ R = \frac{\rho \cdot L}{A} \]
Substituting the values we have:
- \( R = \frac{(3 \times 10^{-7} \, \text{ohm-m}) \cdot (1 \, \text{m})}{0.0001 \, \text{m}^2} \)

### Step 5: Simplify the calculation
Calculating the resistance:
- \( R = \frac{3 \times 10^{-7}}{0.0001} \)
- \( R = 3 \times 10^{-7} \times 10^4 \)
- \( R = 3 \times 10^{-3} \, \text{ohm} \)

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

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