The charge of an electron is `1.6 xx 10^(-19)` coulomb. How many electrons per seconds pass through a cross section of a Cu wir carrying `10^(-6)` amp ?

Options

A. 300
B. 1800
C. 1200
D. 600

Answer

To solve the problem of how many electrons pass through a cross section of a copper wire carrying a current of \(10^{-6}\) amperes, we can use the relationship between current, charge, and time.

### Step-by-Step Solution:

1. **Understand the relationship between current, charge, and time**:
The formula for current (I) is given by:
\[ I = \frac{Q}{t} \]
where \(I\) is the current in amperes, \(Q\) is the charge in coulombs, and \(t\) is the time in seconds.

2. **Rearranging the formula**:
We can rearrange this formula to find the charge passing through a cross-section per second:
\[ Q = I \times t \]
For our case, since we want to find the charge per second, we can set \(t = 1\) second:
\[ Q = I \times 1 = I \]

3. **Substituting the given current**:
We know the current \(I\) is \(10^{-6}\) amperes:
\[ Q = 10^{-6} \text{ coulombs} \]

4. **Finding the number of electrons**:
The charge of a single electron is given as \(1.6 \times 10^{-19}\) coulombs. To find the number of electrons (\(n\)) passing through the wire per second, we can use the formula:
\[ n = \frac{Q}{\text{charge of one electron}} = \frac{Q}{e} \]
Substituting the values we have:
\[ n = \frac{10^{-6}}{1.6 \times 10^{-19}} \]

5. **Calculating the number of electrons**:
Now we perform the division:
\[ n = \frac{10^{-6}}{1.6 \times 10^{-19}} = 6.25 \times 10^{12} \]
Therefore, approximately \(6.25 \times 10^{12}\) electrons pass through the cross-section of the wire each second.

### Final Answer:
Approximately \(6.25 \times 10^{12}\) electrons per second pass through the cross-section of the copper wire carrying \(10^{-6}\) amperes.

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