Current flows through a metallic conductor whose area of cross-section increases in the direction of the current. If we move in this direction.

Options

A. the current will change
B. the carrier density will change
C. the drift velocity will increase
D. the drift velocity will decrease

Explanation

To solve the problem, we need to analyze the situation where current flows through a metallic conductor with an increasing area of cross-section in the direction of the current. We will look into how this affects the current, carrier density, and drift velocity.

### Step-by-Step Solution:

1. **Understanding the Current**:
- The current \( I \) in a conductor is defined by the equation:
\[ I = n \cdot A \cdot e \cdot v_d \]
where:
- \( n \) = carrier density (number of charge carriers per unit volume)
- \( A \) = cross-sectional area of the conductor
- \( e \) = charge of the carrier (for electrons, \( e \approx 1.6 \times 10^{-19} \) C)
- \( v_d \) = drift velocity of the charge carriers.

2. **Current Flowing Through the Conductor**:
- Since the current is flowing through the conductor, we need to consider whether the current \( I \) changes as we move along the conductor. In a steady state, the current remains constant throughout the conductor, regardless of changes in the area of cross-section. Therefore, we conclude:
\[ I = \text{constant} \]

3. **Carrier Density**:
- The carrier density \( n \) is defined as the number of charge carriers per unit volume. In a metallic conductor, this value is typically constant for a given material and does not change with the area of cross-section. Thus, we conclude:
\[ n = \text{constant} \]

4. **Drift Velocity**:
- From the equation \( I = n \cdot A \cdot e \cdot v_d \), we can rearrange it to find the drift velocity:
\[ v_d = \frac{I}{n \cdot A \cdot e} \]
- Since \( I \) and \( n \) are constant, and \( e \) (the charge of the electron) is also constant, we can see that drift velocity \( v_d \) is inversely proportional to the cross-sectional area \( A \):
\[ v_d \propto \frac{1}{A} \]
- As we move in the direction of the current, the area \( A \) increases. Therefore, as \( A \) increases, \( v_d \) must decrease:
\[ v_d \text{ decreases} \]

### Conclusion:
- **Current**: Remains constant.
- **Carrier Density**: Remains constant.
- **Drift Velocity**: Decreases as the area of cross-section increases.