A current of 1 mA is flowing through a copper wire. How many electrons will pass a given point in one second `[e = 1.6 xx 10^(19)`Coulomb]

Options

A. `6.25 xx 10^(19)`
B. `6.25 xx 10^(15)`
C. `6.25 xx 10^(31)`
D. `6.25 xx10^(8)`

Answer

To find the number of electrons passing a given point in one second when a current of 1 mA is flowing through a copper wire, 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 point in a circuit per unit time (t). Mathematically, this is expressed as:
\[ I = \frac{Q}{t} \]

### Step 2: Convert the current from mA to A
Given that the current is 1 mA, we need to convert this to amperes:
\[ 1 \text{ mA} = 1 \times 10^{-3} \text{ A} \]

### Step 3: Calculate the charge flowing in one second
Since we are looking for the charge that flows in one second (t = 1 s), we can rearrange the formula to find Q:
\[ Q = I \times t \]
Substituting the values:
\[ Q = 1 \times 10^{-3} \text{ A} \times 1 \text{ s} = 1 \times 10^{-3} \text{ C} \]

### Step 4: Relate charge to the number of electrons
The charge of a single electron (e) is given as:
\[ e = 1.6 \times 10^{-19} \text{ C} \]
To find the number of electrons (N) that correspond to the total charge (Q), we use the formula:
\[ Q = N \times e \]
Rearranging this gives:
\[ N = \frac{Q}{e} \]

### Step 5: Substitute the values to find N
Now we substitute the values of Q and e into the equation:
\[ N = \frac{1 \times 10^{-3} \text{ C}}{1.6 \times 10^{-19} \text{ C}} \]

### Step 6: Perform the calculation
Calculating N:
\[ N = \frac{1 \times 10^{-3}}{1.6 \times 10^{-19}} = 6.25 \times 10^{15} \]

### Conclusion
Thus, the number of electrons passing a given point in one second is:
\[ N = 6.25 \times 10^{15} \]