A current of 4 A is flowing in a cylindrical conductor. The number of free electrons passing per second through the cross-section of conductor is

Options

A. `2 * 10^(19)`
B. `3 * 10^(20)`
C. `2.5 * 10^(19)`
D. `4 * 10^(18)`

Answer

To find the number of free electrons passing per second through the cross-section of a cylindrical conductor with a current of 4 A, we can follow these steps:

### Step 1: Understand the relationship between current, charge, and time
The current (I) flowing through a conductor is defined as the rate of flow of charge (Q) per unit time (T). Mathematically, this is expressed as:
\[ I = \frac{dQ}{dT} \]

### Step 2: Rearrange the formula to find charge
From the above equation, we can express the total charge (Q) that flows in a given time (T):
\[ Q = I \times T \]

### Step 3: Substitute the known values
In this case, we have:
- Current (I) = 4 A
- Time (T) = 1 second (since we want the number of electrons per second)

Substituting these values into the equation gives:
\[ Q = 4 \, \text{A} \times 1 \, \text{s} = 4 \, \text{C} \]

### Step 4: Relate charge to the number of electrons
The total charge (Q) can also be expressed in terms of the number of electrons (n) and the charge of a single electron (e):
\[ Q = n \times e \]
where the charge of a single electron \( e \) is approximately \( 1.6 \times 10^{-19} \, \text{C} \).

### Step 5: Rearrange to find the number of electrons
We can rearrange the equation to solve for the number of electrons (n):
\[ n = \frac{Q}{e} \]

### Step 6: Substitute the values to find n
Substituting the values we have:
\[ n = \frac{4 \, \text{C}}{1.6 \times 10^{-19} \, \text{C}} \]

### Step 7: Calculate the number of electrons
Calculating this gives:
\[ n = \frac{4}{1.6 \times 10^{-19}} = 2.5 \times 10^{19} \, \text{electrons per second} \]

### Conclusion
Thus, the number of free electrons passing per second through the cross-section of the conductor is:
\[ n = 2.5 \times 10^{19} \, \text{electrons/second} \]