How many electrons consitute a currenet of one microampere ?

Options

A. `6.25 xx 10 ^(6)`
B. `6.25 xx 10 ^(12)`
C. `6.25 xx 10 ^(9)`
D. `6.25 xx 10 ^(15)`

Answer

To find out how many electrons constitute a current of one microampere (1 µA) in one second, we can follow these steps:

### Step 1: Understand the given values
We know that:
- Current (I) = 1 microampere = \(1 \times 10^{-6}\) amperes
- Time (t) = 1 second

### Step 2: Use the formula for electric current
The formula for electric current is given by:
\[ I = \frac{Q}{t} \]
Where:
- \(I\) is the current,
- \(Q\) is the charge,
- \(t\) is the time.

Since we are considering the time to be 1 second, we can rewrite the formula as:
\[ Q = I \times t \]

### Step 3: Substitute the values into the equation
Substituting the values we have:
\[ Q = (1 \times 10^{-6} \, \text{A}) \times (1 \, \text{s}) = 1 \times 10^{-6} \, \text{C} \]

### Step 4: Relate charge to the number of electrons
The charge \(Q\) can also be expressed in terms of the number of electrons (\(n\)) and the charge of a single electron (\(e\)):
\[ Q = n \times e \]
Where:
- \(e\) (the charge of one electron) = \(1.6 \times 10^{-19}\) coulombs.

### Step 5: Rearrange the equation to find the number of electrons
We can rearrange the equation to solve for \(n\):
\[ n = \frac{Q}{e} \]

### Step 6: Substitute the values of \(Q\) and \(e\)
Now substituting the values we have:
\[ n = \frac{1 \times 10^{-6} \, \text{C}}{1.6 \times 10^{-19} \, \text{C/electron}} \]

### Step 7: Calculate the number of electrons
Calculating this gives:
\[ n = \frac{1 \times 10^{-6}}{1.6 \times 10^{-19}} \approx 6.25 \times 10^{12} \]

### Final Answer
Thus, the number of electrons that constitute a current of one microampere in one second is approximately:
\[ n \approx 6.25 \times 10^{12} \, \text{electrons} \]

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