Two parallel plate capacitors X and Y, have the same area of plates and same separation between plates. X has air and Y with dielectric of constant 2 between its plates. They are connected in series to a battery of 12 V. The ratio of electrostatic energy stored in X and Y is

Calculation:
For two capacitors in series, the total potential difference across both capacitors is equal to the battery voltage. The formula for the electrostatic energy stored in a capacitor is given by:

U = (1/2) × C × V²

Where:

• U is the energy stored in the capacitor,
• C is the capacitance,
• V is the voltage across the capacitor.

The capacitance of a parallel plate capacitor is given by:

C = (ε₀ × A) / d

Where:

• ε₀ is the permittivity of free space (for air, it is 1),
• A is the area of the plates,
• d is the separation between the plates.

For capacitor X, the dielectric constant is 1 (for air), and for capacitor Y, the dielectric constant is 2. The capacitance of Y will therefore be twice the capacitance of X. Since the capacitors are in series, the total capacitance is reduced, and the voltage across each capacitor is inversely proportional to their capacitance.

The energy stored in each capacitor depends on its capacitance, and since Y has twice the capacitance of X, the energy stored in X will be half of that stored in Y.

Correct Answer: Option 4 - 1 : 2