The length and area of cross-section of a conductor are doubled, its resistance is

Options

A. unchanged
B. halved
C. doubled
D. quadrupled

Explanation

To solve the problem, we need to understand how the resistance of a conductor changes when its length and area of cross-section are altered. The formula for resistance (R) is given by:

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

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

### Step-by-Step Solution:

1. **Identify the Initial Conditions**:
- Let the initial length of the conductor be \( L \).
- Let the initial area of cross-section be \( A \).
- The initial resistance \( R \) can be expressed as:
\[ R = \frac{\rho L}{A} \]

2. **Determine the New Conditions**:
- According to the problem, both the length and the area of cross-section are doubled:
- New length \( L' = 2L \)
- New area \( A' = 2A \)

3. **Calculate the New Resistance**:
- Substitute the new values into the resistance formula:
\[ R' = \frac{\rho L'}{A'} \]
- Replace \( L' \) and \( A' \) with their expressions:
\[ R' = \frac{\rho (2L)}{2A} \]

4. **Simplify the Expression**:
- The expression simplifies as follows:
\[ R' = \frac{2\rho L}{2A} = \frac{\rho L}{A} \]
- This shows that:
\[ R' = R \]

5. **Conclusion**:
- The new resistance \( R' \) is equal to the original resistance \( R \).

### Final Answer:
The resistance of the conductor remains unchanged, i.e., \( R' = R \).