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. `1.5 xx 10^19`
B. `3.9 xx10^19`
C. `6.75 xx 10^19`
D. `3.75 xx 10^19`

Explanation

To solve the problem, we will use the relationship between current, charge, and time. The formula we will use is:

\[ Q = I \times t \]

where:
- \( Q \) is the charge in coulombs (C),
- \( I \) is the current in amperes (A),
- \( t \) is the time in seconds (s).

### Step 1: Calculate the Charge

Given:
- Current \( I = 0.2 \, A \)
- Time \( t = 30 \, s \)

Using the formula:

\[ Q = I \times t \]
\[ Q = 0.2 \, A \times 30 \, s \]
\[ Q = 6 \, C \]

### Step 2: Calculate the Number of Electrons

To find the number of electrons, we will use the formula:

\[ n = \frac{Q}{e} \]

where:
- \( n \) is the number of electrons,
- \( e \) is the charge of one electron, which is \( 1.6 \times 10^{-19} \, C \).

Now substituting the values:

\[ n = \frac{Q}{e} \]
\[ n = \frac{6 \, C}{1.6 \times 10^{-19} \, C} \]

Calculating the number of electrons:

\[ n = \frac{6}{1.6 \times 10^{-19}} \]
\[ n = 3.75 \times 10^{19} \]

### Final Answers

- The amount of charge that passes through the cross-section of the conductor in 30 seconds is **6 C**.
- The number of electrons that flow in this time interval is approximately **3.75 x 10^19 electrons**.