Two capacitors of capacitances `C_(1) and C_(2)` are connected in parallel. If a charge q is given to the assembly, the charge gets shared. The ratio of the charge on the capacitor `C_(1)` to the charge on `C_(2)` is

Options

A. `(C_(1))/(C_(2))`
B. `(C_(2))/(C_(1))`
C. `C_(1)C_(2)`
D. `(1)/(C_(1)C_(2))`

Explanation

To solve the problem of finding the ratio of the charge on two capacitors connected in parallel, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Configuration**:
- We have two capacitors, \( C_1 \) and \( C_2 \), connected in parallel. When capacitors are connected in parallel, they share the same voltage across their terminals.

2. **Define the Charges**:
- Let \( Q_1 \) be the charge on capacitor \( C_1 \) and \( Q_2 \) be the charge on capacitor \( C_2 \).

3. **Use the Relationship of Voltage and Charge**:
- The voltage across each capacitor can be expressed using the formula:
\[ V = \frac{Q}{C} \]
- For capacitor \( C_1 \):
\[ V = \frac{Q_1}{C_1} \]
- For capacitor \( C_2 \):
\[ V = \frac{Q_2}{C_2} \]

4. **Set the Voltages Equal**:
- Since both capacitors are in parallel, the voltages across them are equal:
\[ \frac{Q_1}{C_1} = \frac{Q_2}{C_2} \]

5. **Rearrange the Equation**:
- Cross-multiplying gives:
\[ Q_1 \cdot C_2 = Q_2 \cdot C_1 \]

6. **Find the Ratio of Charges**:
- Dividing both sides by \( Q_2 \cdot C_1 \) gives:
\[ \frac{Q_1}{Q_2} = \frac{C_1}{C_2} \]

7. **Conclusion**:
- Therefore, the ratio of the charge on capacitor \( C_1 \) to the charge on capacitor \( C_2 \) is:
\[ \frac{Q_1}{Q_2} = \frac{C_1}{C_2} \]

### Final Answer:
The ratio of the charge on capacitor \( C_1 \) to the charge on capacitor \( C_2 \) is \( \frac{C_1}{C_2} \).

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