Two capacitors, one of `4muF` and the other of `5muF`, are connected in parallel and then charged on a 100 V supply. The charge on each capacitor is respectively

Options

A. 0.4 mC and 0.5 mC
B. 0.4 mC and 0.8 mC
C. 4 mC and 5 mC
D. 4 mC and 8 mC

Explanation

To solve the problem of finding the charge on each capacitor when they are connected in parallel to a 100 V supply, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Values of the Capacitors**:
- Capacitor \( C_1 = 4 \, \mu F \)
- Capacitor \( C_2 = 5 \, \mu F \)

2. **Understand the Configuration**:
- The capacitors are connected in parallel. In a parallel connection, the voltage across each capacitor is the same.

3. **Determine the Voltage**:
- The supply voltage \( V = 100 \, V \).

4. **Calculate the Charge on Capacitor \( C_1 \)**:
- The formula for charge \( Q \) on a capacitor is given by:
\[ Q = C \times V \]
- For \( C_1 \):
\[ Q_1 = C_1 \times V = 4 \, \mu F \times 100 \, V \]
- Convert \( \mu F \) to Farads:
\[ Q_1 = 4 \times 10^{-6} \, F \times 100 \, V = 4 \times 10^{-4} \, C \]
- Thus, \( Q_1 = 0.4 \, mC \) (milliCoulombs).

5. **Calculate the Charge on Capacitor \( C_2 \)**:
- For \( C_2 \):
\[ Q_2 = C_2 \times V = 5 \, \mu F \times 100 \, V \]
- Convert \( \mu F \) to Farads:
\[ Q_2 = 5 \times 10^{-6} \, F \times 100 \, V = 5 \times 10^{-4} \, C \]
- Thus, \( Q_2 = 0.5 \, mC \).

6. **Final Answers**:
- The charge on the 4 µF capacitor \( Q_1 = 0.4 \, mC \).
- The charge on the 5 µF capacitor \( Q_2 = 0.5 \, mC \).

### Summary of Charges:
- Charge on \( C_1 \) (4 µF): \( 0.4 \, mC \)
- Charge on \( C_2 \) (5 µF): \( 0.5 \, mC \)

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