The dimensions of a mangnin block are `1 cm xx 1 cm xx100 cm` The electrical resistivity of mangnin is `4.4 xx10^(-7)` ohm–meter. The resistance between the opposite rectangular faces is –

Options

A. `4.4 xx10^(-7)` ohm
B. `4.4 xx10^(-3)` ohm
C. `4.4 xx10^(-5)` ohm
D. `4.4 xx10^(-1)` ohm

Answer

To find the resistance between the opposite rectangular faces of a manganin block with dimensions \(1 \, \text{cm} \times 1 \, \text{cm} \times 100 \, \text{cm}\) and an electrical resistivity of \(4.4 \times 10^{-7} \, \Omega \cdot \text{m}\), we will use the formula for resistance:

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

where:
- \(R\) is the resistance,
- \(\rho\) is the resistivity,
- \(L\) is the length of the conductor,
- \(A\) is the cross-sectional area.

### Step 1: Identify the dimensions
The dimensions of the manganin block are:
- Length (\(L\)) = \(100 \, \text{cm}\)
- Cross-sectional area (\(A\)) = \(1 \, \text{cm} \times 1 \, \text{cm}\)

### Step 2: Convert dimensions to meters
To use the resistivity in ohm-meters, we need to convert the dimensions from centimeters to meters:
- Length (\(L\)) = \(100 \, \text{cm} = 1 \, \text{m}\)
- Cross-sectional area (\(A\)) = \(1 \, \text{cm} \times 1 \, \text{cm} = (0.01 \, \text{m}) \times (0.01 \, \text{m}) = 0.0001 \, \text{m}^2 = 10^{-4} \, \text{m}^2\)

### Step 3: Substitute values into the resistance formula
Now we can substitute the values into the resistance formula:
\[ R = \frac{4.4 \times 10^{-7} \, \Omega \cdot \text{m} \times 1 \, \text{m}}{10^{-4} \, \text{m}^2} \]

### Step 4: Calculate the resistance
Calculating the resistance:
\[ R = \frac{4.4 \times 10^{-7}}{10^{-4}} = 4.4 \times 10^{-3} \, \Omega \]

### Final Answer
The resistance between the opposite rectangular faces of the manganin block is:
\[ R = 4.4 \times 10^{-3} \, \Omega \]

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