A conductor carries a current of `0.2 A`. Find the amount of charge that will pass through the cross-section of the conductor in `30 s`. How many electrons will flow in this time interval if the charge on one electron is `1.6 xx 10^-19 C` ?

Options

A. `0.375xx10^(19)`
B. `375xx10^(19)`
C. `3.75xx10^(19)`
D. `37.5xx10^(19)`

Answer

To solve the problem step by step, we will use the relationship between current, charge, and time, and then calculate the number of electrons based on the charge of a single electron.

### Step 1: Understand the relationship between current, charge, and time.
The formula that relates current (I), charge (Q), and time (T) is given by:
\[ I = \frac{Q}{T} \]
Where:
- \( I \) is the current in amperes (A),
- \( Q \) is the charge in coulombs (C),
- \( T \) is the time in seconds (s).

### Step 2: Rearrange the formula to find the charge.
From the formula, we can rearrange it to find the charge:
\[ Q = I \times T \]

### Step 3: Substitute the known values.
We know:
- Current \( I = 0.2 \, A \)
- Time \( T = 30 \, s \)

Now substituting these values into the equation:
\[ Q = 0.2 \, A \times 30 \, s \]
\[ Q = 6 \, C \]

### Step 4: Calculate the number of electrons.
To find the number of electrons (n) that correspond to this charge, we can use the charge of a single electron, which is:
\[ e = 1.6 \times 10^{-19} \, C \]

The total charge can also be expressed in terms of the number of electrons:
\[ Q = n \times e \]
Where \( n \) is the number of electrons.

### Step 5: Rearrange to find the number of electrons.
Rearranging the equation gives:
\[ n = \frac{Q}{e} \]

### Step 6: Substitute the known values.
Now substituting the values we have:
\[ n = \frac{6 \, C}{1.6 \times 10^{-19} \, C} \]

### Step 7: Perform the calculation.
Calculating \( n \):
\[ n = \frac{6}{1.6 \times 10^{-19}} \]
\[ n = 3.75 \times 10^{19} \]

### Final Result:
Thus, the number of electrons that will flow through the cross-section of the conductor in 30 seconds is:
\[ n = 3.75 \times 10^{19} \]