Two conductors insulated from each other, charged by transferring electrons from one conductor to the other. After `25 xx 10^12` electrons have been transferred. The potential difference between the conductors is found to be 16V. The capacitance of the system is

Options

A. `25 muF`
B. `.25 muF`
C. `25 nF`
D. `25 PF`

Answer

To find the capacitance of the system, we will follow these steps:

### Step 1: Calculate the total charge (Q) transferred
The total charge transferred when electrons are moved can be calculated using the formula:

\[ Q = n \cdot e \]

Where:
- \( n \) = number of electrons transferred = \( 25 \times 10^{12} \)
- \( e \) = charge of one electron = \( 1.6 \times 10^{-19} \, \text{C} \)

Substituting the values:

\[ Q = 25 \times 10^{12} \times 1.6 \times 10^{-19} \]

### Step 2: Perform the multiplication
Calculating \( Q \):

\[ Q = 25 \times 1.6 \times 10^{12} \times 10^{-19} = 40 \times 10^{-7} = 4.0 \times 10^{-6} \, \text{C} \]

### Step 3: Use the capacitance formula
The capacitance \( C \) of a capacitor is given by the formula:

\[ C = \frac{Q}{V} \]

Where:
- \( V \) = potential difference = \( 16 \, \text{V} \)

Substituting the values:

\[ C = \frac{4.0 \times 10^{-6}}{16} \]

### Step 4: Perform the division
Calculating \( C \):

\[ C = 0.25 \times 10^{-6} \, \text{F} \]

### Step 5: Convert to microfarads
To express the capacitance in microfarads:

\[ C = 0.25 \, \mu\text{F} \]

### Final Answer
Thus, the capacitance of the system is:

\[ \boxed{0.25 \, \mu\text{F}} \]

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