If the electronic charge is `1.6 xx 10^(-19) ` C, then the number of electrons passing through a section of wire per second, when the wire carries a current of 2A, is

Options

A. `1.25 xx 10^(17)`
B. `1.6 xx 10^(17) `
C. `1.25 x 10^(19)`
D. `1.6 xx 10^(19)`

Explanation

To find the number of electrons passing through a section of wire per second when the wire carries a current of 2 A, 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 section of wire over time (T). The formula is:
\[ I = \frac{Q}{T} \]

### Step 2: 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):
\[ Q = N \cdot e \]
where \( e = 1.6 \times 10^{-19} \) C (the charge of one electron).

### Step 3: Substitute Q in the current formula
Substituting the expression for Q into the current formula gives:
\[ I = \frac{N \cdot e}{T} \]

### Step 4: Rearrange the formula to find N
To find the number of electrons (N), we can rearrange the equation:
\[ N = \frac{I \cdot T}{e} \]

### Step 5: Substitute the known values
We know:
- Current (I) = 2 A
- Time (T) = 1 second (since we are looking for the number of electrons per second)
- Charge of an electron (e) = \( 1.6 \times 10^{-19} \) C

Now substituting these values into the equation:
\[ N = \frac{2 \, \text{A} \cdot 1 \, \text{s}}{1.6 \times 10^{-19} \, \text{C}} \]

### Step 6: Calculate N
Now we perform the calculation:
\[ N = \frac{2}{1.6 \times 10^{-19}} \]
\[ N = \frac{2}{1.6} \times 10^{19} \]
\[ N = 1.25 \times 10^{19} \]

### Final Answer
The number of electrons passing through a section of wire per second is:
\[ N = 1.25 \times 10^{19} \]

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