Consider these three statements for a capacitor
STATEMENT-1 `:` Capacitance of a capacitor must increase when a dielectric is inserted in between the capacitor plates.
STATEMENT-2 `:` Potential differenece across a charged capacitor must increase if a dielectric is inserted in between the capacitor plates.
STATEMENT-3 `:` Electrostatic energy stored by the capacitor may increase if a dielectric inserted in between the capacitor plates

Options

A. T F F
B. F T F
C. T F T
D. F T T

Answer

To analyze the three statements regarding capacitors, we will evaluate each one based on the principles of electrostatics.

### Step-by-Step Solution:

**Step 1: Evaluate Statement 1**
- **Statement**: Capacitance of a capacitor must increase when a dielectric is inserted in between the capacitor plates.
- **Analysis**: When a dielectric material is inserted between the plates of a capacitor, the capacitance increases. This is because the capacitance \( C \) of a capacitor is given by the formula:
\[ C = \frac{k \cdot \varepsilon_0 \cdot A}{d} \]
where \( k \) is the dielectric constant (greater than 1 for dielectrics), \( \varepsilon_0 \) is the permittivity of free space, \( A \) is the area of the plates, and \( d \) is the separation between the plates. Since \( k > 1 \), the capacitance \( C \) increases.
- **Conclusion**: **True**

**Step 2: Evaluate Statement 2**
- **Statement**: Potential difference across a charged capacitor must increase if a dielectric is inserted in between the capacitor plates.
- **Analysis**: The effect of inserting a dielectric depends on whether the capacitor is connected to a battery or not.
- If the capacitor is disconnected (isolated), the charge \( Q \) remains constant, and the potential difference \( V \) decreases because \( V = \frac{Q}{C} \) and \( C \) increases.
- If the capacitor is connected to a battery, the potential difference remains constant, and the charge can increase.
- **Conclusion**: **False**

**Step 3: Evaluate Statement 3**
- **Statement**: Electrostatic energy stored by the capacitor may increase if a dielectric is inserted in between the capacitor plates.
- **Analysis**: The energy stored in a capacitor is given by:
\[ U = \frac{1}{2} C V^2 \]
- If the capacitor is isolated (disconnected), as the capacitance increases, the potential decreases, and the energy may decrease or remain constant.
- If the capacitor is connected to a battery, the capacitance increases, and since \( V \) remains constant, the energy stored increases because \( U = \frac{1}{2} C V^2 \) increases with \( C \).
- **Conclusion**: **True**

### Final Summary:
- **Statement 1**: True
- **Statement 2**: False
- **Statement 3**: True

Thus, the correct evaluation of the statements is:
1. True
2. False
3. True