If the charge on a capacitor is doubled, the value of its capacitance C will be

Options

A. Doubled
B. Halved
C. Remain the same
D. None of these

Explanation

To solve the question regarding the effect of doubling the charge on a capacitor on its capacitance, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Definition of Capacitance**:
The capacitance \( C \) of a capacitor is defined as the ratio of the charge \( Q \) stored on the capacitor to the potential difference \( V \) across it. Mathematically, this is expressed as:
\[ C = \frac{Q}{V} \]

2. **Consider the Effect of Doubling the Charge**:
If the charge on the capacitor is doubled, we can denote the new charge as \( Q' = 2Q \).

3. **Relate Charge, Capacitance, and Voltage**:
Using the definition of capacitance, we can express the new capacitance \( C' \) when the charge is doubled:
\[ C' = \frac{Q'}{V'} \]
Since \( Q' = 2Q \), we have:
\[ C' = \frac{2Q}{V'} \]

4. **Determine the New Voltage**:
The voltage \( V \) across a capacitor is related to the charge and capacitance by the equation:
\[ V = \frac{Q}{C} \]
If we double the charge, the new voltage \( V' \) can be expressed as:
\[ V' = \frac{Q'}{C} = \frac{2Q}{C} \]

5. **Substituting for New Voltage**:
Now substituting \( V' \) back into the equation for \( C' \):
\[ C' = \frac{2Q}{\frac{2Q}{C}} = C \]

6. **Conclusion**:
From the above steps, we find that the capacitance \( C' \) remains the same as the original capacitance \( C \). Therefore, if the charge on a capacitor is doubled, the value of its capacitance does not change.

### Final Answer:
The value of the capacitance \( C \) remains the same.