When the area of cross-section of a conductor is doubled, its resistance becomes:

Options

A. double
B. half
C. four times
D. one-fourth

Answer

To determine how the resistance of a conductor changes when its area of cross-section is doubled, we can follow these steps:

### 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 area of the cross-section.

2. **Identify the original resistance**:
Let the original area of cross-section be \( A_1 \). Thus, the original resistance \( R_1 \) can be expressed as:
\[ R_1 = \frac{\rho L}{A_1} \]

3. **Determine the new area**:
If the area of cross-section is doubled, the new area \( A_2 \) will be:
\[ A_2 = 2A_1 \]

4. **Calculate the new resistance**:
Using the new area \( A_2 \), the new resistance \( R_2 \) can be expressed as:
\[ R_2 = \frac{\rho L}{A_2} = \frac{\rho L}{2A_1} \]

5. **Relate the new resistance to the original resistance**:
We can express \( R_2 \) in terms of \( R_1 \):
\[ R_2 = \frac{1}{2} \cdot \frac{\rho L}{A_1} = \frac{1}{2} R_1 \]

6. **Conclusion**:
Since \( R_1 \) is the original resistance, we find that:
\[ R_2 = \frac{R_1}{2} \]
This means that when the area of cross-section of the conductor is doubled, its resistance becomes half of the original resistance.

### Final Answer:
When the area of cross-section of a conductor is doubled, its resistance becomes **half**.

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