A steady current of 1A is flowing through the conductor. The number of electrons flowing through the cross-section of the conductor in 1 sec is :

Options

A. `6.25 xx 10^15`
B. `6.25 xx 10^17`
C. `6.25 xx 10^19`
D. `6.25 xx 10^18`

Answer

To find the number of electrons flowing through the cross-section of a conductor in 1 second when a steady current of 1 A is flowing, we can follow these steps:

### Step 1: Understand the relationship between current, charge, and time
The current (I) is defined as the rate of flow of charge (Q) through a cross-section of the conductor over time (T). This can be expressed with the formula:
\[ I = \frac{Q}{T} \]
Where:
- \( I \) is the current in amperes (A)
- \( Q \) is the charge in coulombs (C)
- \( T \) is the time in seconds (s)

### Step 2: Calculate the charge flowing in 1 second
Given that the current \( I = 1 \, \text{A} \) and the time \( T = 1 \, \text{s} \), we can rearrange the formula to find the charge:
\[ Q = I \times T \]
Substituting the known values:
\[ Q = 1 \, \text{A} \times 1 \, \text{s} = 1 \, \text{C} \]

### Step 3: Relate charge to the number of electrons
The charge of a single electron (e) is approximately:
\[ e = 1.6 \times 10^{-19} \, \text{C} \]
The total charge (Q) can also be expressed in terms of the number of electrons (N) as:
\[ Q = N \times e \]
Where:
- \( N \) is the number of electrons

### Step 4: Solve for the number of electrons
From the equation \( Q = N \times e \), we can solve for \( N \):
\[ N = \frac{Q}{e} \]
Substituting the values we have:
\[ N = \frac{1 \, \text{C}}{1.6 \times 10^{-19} \, \text{C}} \]

### Step 5: Calculate the number of electrons
Calculating \( N \):
\[ N = \frac{1}{1.6 \times 10^{-19}} \approx 6.25 \times 10^{18} \]

### Conclusion
The number of electrons flowing through the cross-section of the conductor in 1 second is approximately:
\[ N \approx 6.25 \times 10^{18} \]