The current of a conductor following through a conductor in terms of the drift speed of electrons is (the symbols have their usual meanings)

Options

A. (a)`I=sqrt(nAe)vd`
B. (b)`I=Asqrt("ne")vd`
C. (c)`I=("ne")/(Avd)`
D. (d)`I="ne"Avd`

Answer

To find the current flowing through a conductor in terms of the drift speed of electrons, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding Current**:
Current (I) is defined as the rate of flow of charge. Mathematically, it can be expressed as:
\[ I = \frac{Q}{t} \]
where \(Q\) is the charge and \(t\) is the time.

2. **Charge Carriers**:
In a conductor, the charge carriers are electrons. The charge of a single electron is denoted by \(e\) (approximately \(1.6 \times 10^{-19}\) coulombs).

3. **Electron Density**:
Let \(n\) be the number density of electrons, which is defined as the number of electrons per unit volume (in \(m^{-3}\)).

4. **Drift Velocity**:
The drift velocity (\(v_d\)) is the average velocity that a charge carrier, such as an electron, attains due to an electric field.

5. **Calculating Charge Flow**:
The volume of the conductor can be expressed as the product of its cross-sectional area (\(A\)) and the drift distance over time (\(v_d \cdot t\)). Therefore, the volume of electrons flowing through the cross-section in time \(t\) is:
\[ V = A \cdot v_d \cdot t \]

6. **Total Number of Electrons**:
The total number of electrons (\(N\)) flowing through the cross-section in time \(t\) can be calculated as:
\[ N = n \cdot V = n \cdot (A \cdot v_d \cdot t) \]

7. **Total Charge**:
The total charge (\(Q\)) flowing through the conductor in time \(t\) is given by:
\[ Q = N \cdot e = n \cdot (A \cdot v_d \cdot t) \cdot e \]

8. **Substituting into Current Formula**:
Now substituting \(Q\) into the current formula:
\[ I = \frac{Q}{t} = \frac{n \cdot (A \cdot v_d \cdot t) \cdot e}{t} \]
This simplifies to:
\[ I = n \cdot A \cdot v_d \cdot e \]

9. **Final Expression**:
Therefore, the current flowing through a conductor in terms of the drift speed of electrons is:
\[ I = n \cdot A \cdot v_d \cdot e \]