How is the current flowing in a conductor changed if the resistance of conductor is doubled keeping the potential difference across it the same ?

Answer

To solve the problem of how the current flowing in a conductor changes when the resistance is doubled while keeping the potential difference constant, we can use Ohm's Law, which states:

\[ V = I \times R \]

where:
- \( V \) is the potential difference (voltage),
- \( I \) is the current,
- \( R \) is the resistance.

### Step-by-Step Solution:

1. **Understand Ohm's Law**: According to Ohm's Law, the relationship between voltage, current, and resistance is given by the equation \( V = I \times R \).

2. **Set up the initial conditions**: Let the initial resistance be \( R_1 \) and the initial current be \( I_1 \). Therefore, we can write:
\[ V = I_1 \times R_1 \]

3. **Consider the new conditions**: If the resistance is doubled, the new resistance \( R_2 \) can be expressed as:
\[ R_2 = 2 \times R_1 \]

4. **Apply Ohm's Law to the new conditions**: With the new resistance, the current \( I_2 \) can be expressed as:
\[ V = I_2 \times R_2 \]

5. **Equate the two expressions for voltage**: Since the potential difference \( V \) remains the same, we can set the two equations equal to each other:
\[ I_1 \times R_1 = I_2 \times (2 \times R_1) \]

6. **Simplify the equation**: We can cancel \( R_1 \) from both sides (assuming \( R_1 \neq 0 \)):
\[ I_1 = I_2 \times 2 \]

7. **Rearrange to find the relationship between \( I_1 \) and \( I_2 \)**: This gives us:
\[ I_2 = \frac{I_1}{2} \]

### Conclusion:
When the resistance of the conductor is doubled while keeping the potential difference constant, the current flowing through the conductor becomes half of the initial current.

### Final Answer:
If the resistance is doubled, the current becomes half of the initial current.