When the length and area of cross-section both are doubled, then its resistance

Options

A. unchanged
B. halved
C. daubled
D. qualdraupled

Answer

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.

### Step-by-Step Solution:

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

2. **Identify the Initial Conditions**:
Let's denote the initial length of the conductor as \( L \) and the initial area of cross-section as \( A \). Therefore, the initial resistance \( R_1 \) can be expressed as:
\[ R_1 = \frac{\rho L}{A} \]

3. **Change the Length and Area**:
According to the problem, both the length and area of the conductor are doubled. Thus:
- New length \( L' = 2L \)
- New area \( A' = 2A \)

4. **Calculate the New Resistance**:
Using the new values in the resistance formula, we get the new resistance \( R_2 \):
\[ R_2 = \frac{\rho L'}{A'} = \frac{\rho (2L)}{2A} \]

5. **Simplify the Expression**:
Simplifying the expression for \( R_2 \):
\[ R_2 = \frac{\rho (2L)}{2A} = \frac{\rho L}{A} \]
This shows that:
\[ R_2 = R_1 \]

6. **Conclusion**:
Since the new resistance \( R_2 \) is equal to the initial resistance \( R_1 \), we conclude that the resistance remains unchanged when both the length and the area of cross-section are doubled.

### Final Answer:
The resistance remains unchanged.