A copper wire of cross - sectional area 3.4 `m m^(2)` and length of the wire 400m, specific resistivity of copper is `1.7xx10^(-8)Omega-m`. Then the resistance of the wire is

Options

A. `20Omega`
B. `200Omega`
C. `2Omega`
D. `2kOmega`

Answer

To find the resistance of a copper wire, we can use the formula for resistance in terms of resistivity:

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

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

### Step 1: Convert the cross-sectional area from mm² to m²
The cross-sectional area is given as \( 3.4 \, \text{mm}^2 \). To convert this to square meters, we use the conversion factor \( 1 \, \text{mm}^2 = 10^{-6} \, \text{m}^2 \):

\[ A = 3.4 \, \text{mm}^2 = 3.4 \times 10^{-6} \, \text{m}^2 \]

### Step 2: Identify the values
From the problem, we have:
- Length \( L = 400 \, \text{m} \)
- Specific resistivity \( \rho = 1.7 \times 10^{-8} \, \Omega \cdot \text{m} \)
- Cross-sectional area \( A = 3.4 \times 10^{-6} \, \text{m}^2 \)

### Step 3: Substitute the values into the resistance formula
Now, we can substitute the values into the resistance formula:

\[ R = \frac{(1.7 \times 10^{-8}) \cdot (400)}{3.4 \times 10^{-6}} \]

### Step 4: Calculate the numerator
First, calculate the numerator:

\[ 1.7 \times 10^{-8} \cdot 400 = 6.8 \times 10^{-6} \]

### Step 5: Calculate the resistance
Now substitute the numerator back into the resistance formula:

\[ R = \frac{6.8 \times 10^{-6}}{3.4 \times 10^{-6}} = 2 \, \Omega \]

### Final Answer
Thus, the resistance of the wire is:

\[ R = 2 \, \Omega \]