Capacitor of capacitance C with oil between the plates of dielectric constant 2. If oil is removed, the capacitance is .

Options

A. 2 C
B. `sqrt2 C`
C. `(C )/(sqrt2 )`
D. `(C )/(2)`

Explanation

To solve the problem, we need to understand how the capacitance of a capacitor changes when a dielectric material is introduced and then removed.

### Step-by-Step Solution:

1. **Understanding Capacitance with Dielectric**:
- The capacitance \( C \) of a capacitor with a dielectric material is given by the formula:
\[ C' = K \cdot C \]
where \( C' \) is the new capacitance with the dielectric, \( K \) is the dielectric constant, and \( C \) is the original capacitance without the dielectric.

2. **Given Values**:
- The dielectric constant \( K \) is given as 2.
- Therefore, when the oil (dielectric) is present, the capacitance becomes:
\[ C' = 2C \]

3. **Removing the Dielectric**:
- When the dielectric is removed, the capacitance returns to its original value:
\[ C'' = \frac{C'}{K} \]
- Substituting \( C' = 2C \) and \( K = 2 \):
\[ C'' = \frac{2C}{2} = C \]

4. **Conclusion**:
- The capacitance after the oil is removed is \( C \).

### Final Answer:
The capacitance after the oil is removed is \( C \).