The dimensions of a block are `1cmxx1cmxx100cm.` If the specific resistance of its material is `2xx10^(-7) ohmxxmetre`, then the resistance between the opposite rectangular faces is

Options

A. `2xx10^(-9) Omega`
B. `2xx10^(-7) Omega`
C. `2xx10^(-5) Omega`
D. `2xx10^(-3) Omega`

Explanation

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 block (the distance between the two opposite faces),
- \( A \) is the cross-sectional area of the block.

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

### Step 2: Convert dimensions to meters
To use the resistivity value given in ohm-meters, we need to convert all dimensions from centimeters to meters:
- Length \( l = 100 \, \text{cm} = 100 \times 10^{-2} \, \text{m} = 1 \, \text{m} \)
- Width \( w = 1 \, \text{cm} = 1 \times 10^{-2} \, \text{m} = 0.01 \, \text{m} \)
- Height \( h = 1 \, \text{cm} = 1 \times 10^{-2} \, \text{m} = 0.01 \, \text{m} \)

### Step 3: Calculate the cross-sectional area \( A \)
The cross-sectional area \( A \) is given by the product of width and height:
\[ A = w \times h = (0.01 \, \text{m}) \times (0.01 \, \text{m}) = 0.0001 \, \text{m}^2 \]

### Step 4: Use the specific resistance value
The specific resistance \( \rho \) is given as:
\[ \rho = 2 \times 10^{-7} \, \Omega \cdot \text{m} \]

### Step 5: Substitute values into the resistance formula
Now we can substitute the values into the resistance formula:
\[ R = \frac{\rho l}{A} = \frac{(2 \times 10^{-7} \, \Omega \cdot \text{m}) \times (1 \, \text{m})}{0.0001 \, \text{m}^2} \]

### Step 6: Calculate the resistance
Calculating the above expression gives:
\[ R = \frac{2 \times 10^{-7}}{0.0001} = \frac{2 \times 10^{-7}}{10^{-4}} = 2 \times 10^{-3} \, \Omega \]

### Final Answer
The resistance between the opposite rectangular faces is:
\[ R = 2 \times 10^{-3} \, \Omega \]

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