A copper cylindrical tube has inner radius a and outer radius b. The resistivity is p. The resistance of . the cylinder between the two ends is

Options

A. `(rhol)/(b^(2)-a^(2))`
B. `(rhol)/(2pi(b-a)`
C. `(rhol)/(pi(b^(2)-a^(2))`
D. `(pi(b^(2)-a^(2)))/(rhol)`

Explanation

To find the resistance of a copper cylindrical tube with inner radius \( a \), outer radius \( b \), and resistivity \( \rho \), we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Geometry**:
The cylindrical tube has two radii: an inner radius \( a \) and an outer radius \( b \). The length of the cylinder is denoted as \( L \).

2. **Resistance Formula**:
The resistance \( R \) of a conductor is given by the formula:
\[ R = \frac{\rho L}{A} \]
where \( \rho \) is the resistivity, \( L \) is the length of the conductor, and \( A \) is the cross-sectional area.

3. **Determine the Cross-Sectional Area**:
Since we have a hollow cylinder, the cross-sectional area \( A \) is the area of the outer circle minus the area of the inner circle:
\[ A = \pi b^2 - \pi a^2 \]
This can be factored as:
\[ A = \pi (b^2 - a^2) \]

4. **Substituting the Area into the Resistance Formula**:
Now, substitute the expression for the area \( A \) back into the resistance formula:
\[ R = \frac{\rho L}{\pi (b^2 - a^2)} \]

5. **Final Expression for Resistance**:
Therefore, the resistance of the cylindrical tube between the two ends is:
\[ R = \frac{\rho L}{\pi (b^2 - a^2)} \]