The drift velocity of electrons for a conductor connected in an electrical circuit is `V_(a)`.The conductor in now replaced by another conductor with same material and same length but double the area of cross section. The applied voltage remains same.The new drift velocity of electrons will be

Options

A. `(V_(d))/(4)`
B. `(V_(d))/(2)`
C. `2V_(d)`
D. `V_(d)`

Answer

To solve the problem, we need to analyze the relationship between drift velocity, electric field, and the physical properties of the conductor.

### Step-by-Step Solution:

1. **Understanding Drift Velocity**:
The drift velocity \( V_d \) of electrons in a conductor is defined by the equation:
\[ V_d = \frac{I}{nAq} \]
where:
- \( I \) is the current,
- \( n \) is the number density of charge carriers (electrons),
- \( A \) is the cross-sectional area of the conductor,
- \( q \) is the charge of an electron.

2. **Current and Voltage Relationship**:
The current \( I \) in a conductor can also be expressed using Ohm's law:
\[ I = \frac{V}{R} \]
where \( V \) is the voltage and \( R \) is the resistance. The resistance \( R \) of a conductor is given by:
\[ R = \frac{\rho L}{A} \]
where:
- \( \rho \) is the resistivity of the material,
- \( L \) is the length of the conductor,
- \( A \) is the cross-sectional area.

3. **Replacing the Conductor**:
In this problem, we replace the original conductor with another conductor of the same material and length but with double the cross-sectional area \( (A' = 2A) \). The applied voltage \( V \) remains the same.

4. **Effect on Resistance**:
The new resistance \( R' \) of the conductor with double the area becomes:
\[ R' = \frac{\rho L}{A'} = \frac{\rho L}{2A} = \frac{R}{2} \]
This means the new resistance is half of the original resistance.

5. **Current in the New Conductor**:
Since the voltage remains the same, the new current \( I' \) can be calculated as:
\[ I' = \frac{V}{R'} = \frac{V}{\frac{R}{2}} = 2 \cdot \frac{V}{R} = 2I \]
Thus, the current doubles when the cross-sectional area is doubled.

6. **Calculating New Drift Velocity**:
Now, substituting the new current \( I' \) into the drift velocity equation:
\[ V_d' = \frac{I'}{nA'q} = \frac{2I}{n(2A)q} = \frac{I}{nAq} = V_d \]
Therefore, the new drift velocity \( V_d' \) remains the same as the original drift velocity \( V_d \).

### Final Answer:
The new drift velocity of electrons will be:
\[ V_d' = V_d \]