A wire of certain cross-section carrying a current of 2 ampere. The number of electrons flowing through the wire is:

Options

A. `2.25 xx 10^(19)`
B. `6.25 xx 10^(19)`
C. `1.25 xx 10^(19)`
D. `0.25 xx 10^(19)`

Explanation

To solve the problem of finding the number of electrons flowing through a wire carrying a current of 2 amperes, we can follow these steps:

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

### Step 2: Relate charge to the number of electrons.
The total charge (Q) can be expressed in terms of the number of electrons (n) and the charge of a single electron (e):
\[ Q = n \cdot e \]
where \( e \) (the charge of an electron) is approximately \( 1.6 \times 10^{-19} \) coulombs.

### Step 3: Substitute the expression for charge into the current formula.
We can rewrite the current equation using the expression for charge:
\[ I = \frac{n \cdot e}{t} \]

### Step 4: Rearrange the equation to find the number of electrons per unit time.
Since we want to find the number of electrons flowing through the wire per unit time, we can rearrange the equation:
\[ n = \frac{I \cdot t}{e} \]

### Step 5: Calculate the number of electrons per second.
Since we are interested in the number of electrons flowing per unit time (per second), we can set \( t = 1 \) second:
\[ n = \frac{I}{e} \]
Substituting the values:
- \( I = 2 \) amperes
- \( e = 1.6 \times 10^{-19} \) coulombs

We get:
\[ n = \frac{2}{1.6 \times 10^{-19}} \]

### Step 6: Perform the calculation.
Calculating the above expression:
\[ n = \frac{2}{1.6 \times 10^{-19}} = 1.25 \times 10^{19} \]

### Conclusion:
Thus, the number of electrons flowing through the wire per second is:
\[ n = 1.25 \times 10^{19} \]

### Final Answer:
The number of electrons flowing through the wire is \( 1.25 \times 10^{19} \).

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