If the potential difference V applied across a conductor is increased to 2V with its temperature kept constant, the drift velocity of the free electrons in a conductor will-

Options

A. remain the same
B. become half of its previous value
C. be double of its initial value
D. become zero.

Answer

To solve the problem of how the drift velocity of free electrons in a conductor changes when the potential difference is increased to 2V while keeping the temperature constant, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding Drift Velocity**:
The drift velocity (\(v_d\)) of free electrons in a conductor is the average velocity that the electrons attain due to the electric field applied across the conductor.

2. **Current and Drift Velocity Relationship**:
The current (\(I\)) flowing through the conductor can be expressed in terms of drift velocity as:
\[ I = n \cdot e \cdot A \cdot v_d \]
where:
- \(n\) = number of charge carriers per unit volume,
- \(e\) = charge of an electron,
- \(A\) = cross-sectional area of the conductor,
- \(v_d\) = drift velocity.

3. **Ohm's Law**:
According to Ohm's Law, the relationship between voltage (\(V\)), current (\(I\)), and resistance (\(R\)) is given by:
\[ V = I \cdot R \]
Since the temperature is kept constant, the resistance \(R\) remains constant.

4. **Proportionality of Voltage and Current**:
From Ohm's Law, if the voltage is increased, the current will also increase proportionally as long as the resistance remains constant:
\[ V \propto I \]

5. **Implication for Drift Velocity**:
Since \(I\) is directly proportional to \(v_d\) (from the drift velocity equation), we can conclude that:
\[ V \propto v_d \]
This means that if the voltage is increased, the drift velocity will also increase.

6. **Calculating the New Drift Velocity**:
If the potential difference is increased from \(V\) to \(2V\), we can express this relationship as:
\[ v_d' = k \cdot (2V) = 2 \cdot (k \cdot V) = 2v_d \]
where \(v_d\) is the initial drift velocity and \(v_d'\) is the new drift velocity after the increase in voltage.

7. **Conclusion**:
Therefore, when the potential difference is increased to 2V, the drift velocity of the free electrons in the conductor will also double.

### Final Answer:
The drift velocity of the free electrons in the conductor will double when the potential difference is increased to 2V.

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