A conductor carries a current of 3mA. The number of electrons passing through it in one minute is about

Options

A. `10^(18)`
B. `10^(20)`
C. `10 ^(23)`
D. `10 ^(25)`

Explanation

To find the number of electrons passing through a conductor carrying a current of 3 mA in one minute, we can follow these steps:

### Step 1: Convert the current from mA to A
The current given is 3 mA. We need to convert this to amperes (A):
\[ 3 \, \text{mA} = 3 \times 10^{-3} \, \text{A} \]

### Step 2: Convert the time from minutes to seconds
We know that 1 minute is equal to 60 seconds. Therefore, the time \( t \) in seconds is:
\[ t = 1 \, \text{minute} = 60 \, \text{seconds} \]

### Step 3: Use the formula for charge
The relationship between current (I), charge (Q), and time (t) is given by:
\[ I = \frac{Q}{t} \]
From this, we can rearrange to find the total charge \( Q \):
\[ Q = I \times t \]

### Step 4: Substitute the values into the formula
Now we can substitute the values of current and time into the equation:
\[ Q = (3 \times 10^{-3} \, \text{A}) \times (60 \, \text{s}) = 0.18 \, \text{C} \]

### Step 5: Calculate the number of electrons
The charge of a single electron \( e \) is approximately \( 1.6 \times 10^{-19} \, \text{C} \). The number of electrons \( n \) can be calculated using the formula:
\[ n = \frac{Q}{e} \]
Substituting the values we have:
\[ n = \frac{0.18 \, \text{C}}{1.6 \times 10^{-19} \, \text{C/electron}} \]

### Step 6: Perform the calculation
Calculating the above expression:
\[ n = \frac{0.18}{1.6 \times 10^{-19}} \approx 1.125 \times 10^{18} \]

### Step 7: Round the result
Rounding \( 1.125 \times 10^{18} \) gives us approximately:
\[ n \approx 10^{18} \]

### Final Answer
The number of electrons passing through the conductor in one minute is about \( 10^{18} \).

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