When current is 4 A in a conductor the drift velocity is `v_(d)` When the current is 3 A the drift velocity will be

Options

A. `(3)/(4)v_(d)`
B. `v_(d)`
C. `(4)/(3)v_(d)`
D. None of these

Answer

To solve the problem, we will use the relationship between current (I) and drift velocity (v_d) in a conductor.

### Step-by-Step Solution:

1. **Understand the relationship**: The current (I) in a conductor is directly proportional to the drift velocity (v_d). This can be expressed mathematically as:
\[ I = N \cdot e \cdot A \cdot v_d \]
where:
- \(I\) = current
- \(N\) = number of charge carriers per unit volume
- \(e\) = charge of an electron
- \(A\) = cross-sectional area of the conductor
- \(v_d\) = drift velocity

2. **Set up the proportion**: Since current is directly proportional to drift velocity, we can write:
\[ \frac{I_1}{I_2} = \frac{v_{d1}}{v_{d2}} \]
where:
- \(I_1 = 4 \, \text{A}\) (current when drift velocity is \(v_d\))
- \(I_2 = 3 \, \text{A}\) (current when we want to find the new drift velocity)
- \(v_{d1} = v_d\) (initial drift velocity)
- \(v_{d2}\) = drift velocity when current is 3 A (what we want to find)

3. **Substitute the values**: Plugging in the known values into the proportion gives:
\[ \frac{4}{3} = \frac{v_d}{v_{d2}} \]

4. **Cross-multiply to solve for \(v_{d2}\)**:
\[ 4 \cdot v_{d2} = 3 \cdot v_d \]

5. **Isolate \(v_{d2}\)**:
\[ v_{d2} = \frac{3}{4} v_d \]

### Final Answer:
When the current is 3 A, the drift velocity \(v_{d2}\) will be \(\frac{3}{4} v_d\).

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