When the current i is flowing through a conductor, the drift velocity is v . If 2i current is flowed through the same metal but having double the area of cross-section, then the drift velocity will be

Options

A. v/4
B. v/2
C. v
D. 4v

Answer

To solve the problem, we will use the relationship between current, drift velocity, and the area of cross-section of the conductor.

### Step-by-Step Solution:

1. **Understand the relationship between current, drift velocity, and area**:
The current \( I \) flowing through a conductor can be expressed using the formula:
\[ I = n \cdot e \cdot A \cdot v_d \]
where:
- \( n \) = number density of charge carriers (electrons),
- \( e \) = charge of an electron,
- \( A \) = area of cross-section,
- \( v_d \) = drift velocity.

2. **Set up the initial condition**:
Let the initial current be \( I = i \) and the initial drift velocity be \( v_d = v \). Thus, we can write:
\[ i = n \cdot e \cdot A \cdot v \]

3. **Consider the new conditions**:
Now, we have a new current \( I' = 2i \) flowing through the same metal but with double the area of cross-section \( A' = 2A \). We need to find the new drift velocity \( v_d' \).

4. **Write the equation for the new current**:
Using the same formula for the new conditions:
\[ I' = n \cdot e \cdot A' \cdot v_d' \]
Substituting \( A' = 2A \) and \( I' = 2i \):
\[ 2i = n \cdot e \cdot (2A) \cdot v_d' \]

5. **Relate the two equations**:
From the first equation, we have:
\[ i = n \cdot e \cdot A \cdot v \]
Now, substituting this into the equation for \( I' \):
\[ 2(n \cdot e \cdot A \cdot v) = n \cdot e \cdot (2A) \cdot v_d' \]

6. **Simplify the equation**:
Cancel \( n \cdot e \) from both sides (assuming \( n \) and \( e \) are constants):
\[ 2A \cdot v = 2A \cdot v_d' \]
Dividing both sides by \( 2A \):
\[ v = v_d' \]

7. **Conclusion**:
The new drift velocity \( v_d' \) is equal to the original drift velocity \( v \):
\[ v_d' = v \]

### Final Answer:
The drift velocity when \( 2i \) current is flowed through the same metal with double the area of cross-section is \( v \).