A potential difference is applied across the ends of a metallic wire. If the potential difference is doubled, the drift velocity will

Options

A. be doubled
B. be halved
C. be quadrupled
D. remain unchanged

Explanation

To solve the question regarding the effect of doubling the potential difference on the drift velocity in a metallic wire, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Relationship**: The drift velocity (\(V_d\)) of charge carriers in a conductor is related to the electric field (\(E\)) produced by the potential difference (\(V\)) across the wire. The relationship can be expressed as:
\[ V_d \propto E \]

2. **Express Electric Field**: The electric field (\(E\)) in the wire can be defined as:
\[ E = \frac{V}{L} \]
where \(L\) is the length of the wire.

3. **Substitute Electric Field into Drift Velocity**: Since the drift velocity is proportional to the electric field, we can write:
\[ V_d \propto \frac{V}{L} \]

4. **Consider Doubling the Potential Difference**: If the potential difference is doubled, we can represent this as:
\[ V' = 2V \]

5. **Recalculate the Drift Velocity**: Substituting the new potential difference into the equation for drift velocity gives:
\[ V_d' \propto \frac{V'}{L} = \frac{2V}{L} \]
This indicates that the new drift velocity (\(V_d'\)) is:
\[ V_d' = 2 \cdot V_d \]

6. **Conclusion**: Therefore, if the potential difference is doubled, the drift velocity will also double.

### Final Answer:
The drift velocity will be doubled.

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