The drift velocity of a current carrying conductor is v. What will be the drift velocity if the current flowing through the wire is doubled?

Options

A. `v//10`
B. `v//2`
C. `2v`
D. `10v`

Explanation

To solve the problem, we need to understand the relationship between current (I) and drift velocity (v_d) in a conductor. The relationship is given by the formula:

\[ I = n \cdot A \cdot e \cdot v_d \]

Where:
- \( I \) is the current,
- \( n \) is the number of charge carriers per unit volume,
- \( A \) is the cross-sectional area of the conductor,
- \( e \) is the charge of an electron,
- \( v_d \) is the drift velocity.

### Step-by-Step Solution:

1. **Understand the Initial Condition**:
- We are given that the initial drift velocity is \( v_d = v \).

2. **Current and Drift Velocity Relationship**:
- According to the formula \( I = n \cdot A \cdot e \cdot v_d \), we can see that the current \( I \) is directly proportional to the drift velocity \( v_d \) when \( n \), \( A \), and \( e \) are constant.

3. **Doubling the Current**:
- If the current is doubled, we can express this as:
\[ I' = 2I \]
- Since \( I \) is proportional to \( v_d \), we can write:
\[ I' = n \cdot A \cdot e \cdot v_d' \]
- Where \( v_d' \) is the new drift velocity after the current is doubled.

4. **Setting Up the Equation**:
- From the proportional relationship, we have:
\[ 2I = n \cdot A \cdot e \cdot v_d' \]
- Substituting the initial current \( I = n \cdot A \cdot e \cdot v \):
\[ 2(n \cdot A \cdot e \cdot v) = n \cdot A \cdot e \cdot v_d' \]

5. **Simplifying the Equation**:
- We can cancel \( n \cdot A \cdot e \) from both sides (assuming they are not zero):
\[ 2v = v_d' \]

6. **Conclusion**:
- Therefore, if the current is doubled, the new drift velocity \( v_d' \) becomes:
\[ v_d' = 2v \]

### Final Answer:
The drift velocity when the current is doubled will be \( 2v \).