The external diameter of a 314 m long copper tube is 1.2 cm and the internal diameter is 1 cm. calculate its resistance if the specific resistance of copper is `2.2xx10^(-8)` ohm-metre.

Options

A. `vec(p)_(1) = a_(1) hat(i) + b_(1) hat(j) + c_(1) hat(k)`
`vec(p)_(2) = a_(2)hat(i) + b_(2) hat(j)`
B. `vec(p)_(1) = c_(1) hat(k)`
`vec(p)_(2) = c_(2)hat(k)`
C. `vec(p)_(1) = a_(1) hat(i) - b_(1) hat(j) + c_(1)hat(k)`
`vec(p)_(2) = a_(2)hat(i) + b_(2) hat(j) - c_(2) hat(k)`
D. `vec(p)_(1) = a_(1)hat(i) + b_(1) hat(j)`
`vec(p)_(2) = a_(2) hat(i) + b_(1) hat(j)`

Explanation

To calculate the resistance of the copper tube, we will follow these steps:

### Step 1: Convert Diameters from cm to m
Given:
- External diameter \( D_1 = 1.2 \, \text{cm} = 1.2 \times 10^{-2} \, \text{m} \)
- Internal diameter \( D_2 = 1 \, \text{cm} = 1.0 \times 10^{-2} \, \text{m} \)

### Step 2: Calculate the Length of the Tube
The length \( L \) of the tube is given as:
- \( L = 314 \, \text{m} \)

### Step 3: Calculate the Cross-Sectional Area
The cross-sectional area \( A \) of the tube can be calculated using the formula for the area of a circle:
\[ A = \pi \left( \frac{D_1}{2} \right)^2 - \pi \left( \frac{D_2}{2} \right)^2 \]
Substituting the values:
\[ A = \pi \left( \frac{1.2 \times 10^{-2}}{2} \right)^2 - \pi \left( \frac{1.0 \times 10^{-2}}{2} \right)^2 \]
Calculating the areas:
\[ A = \pi \left( 0.006 \right)^2 - \pi \left( 0.005 \right)^2 \]
\[ A = \pi (3.6 \times 10^{-5} - 2.5 \times 10^{-5}) = \pi (1.1 \times 10^{-5}) \]
\[ A \approx 3.46 \times 10^{-5} \, \text{m}^2 \]

### Step 4: Use the Resistance Formula
The resistance \( R \) of the tube can be calculated using the formula:
\[ R = \frac{\rho L}{A} \]
Where:
- \( \rho = 2.2 \times 10^{-8} \, \Omega \cdot \text{m} \)
- \( L = 314 \, \text{m} \)
- \( A \approx 3.46 \times 10^{-5} \, \text{m}^2 \)

Substituting the values:
\[ R = \frac{2.2 \times 10^{-8} \times 314}{3.46 \times 10^{-5}} \]
Calculating the resistance:
\[ R \approx \frac{6.908 \times 10^{-6}}{3.46 \times 10^{-5}} \approx 0.199 \, \Omega \]

### Step 5: Final Result
Thus, the resistance of the copper tube is approximately:
\[ R \approx 0.2 \, \Omega \]

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