Two parallel plate capacitors, X and Y, have the same area of plates and the same separation between them. They are connected in series across a 12 V battery. X has air between the plates while Y contains a dielectric medium of dielectric constant 4. The ratio of electrostatic energy stored in X and Y is
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → 4 : 1
Capacitors in series carry the same charge \( Q \). So the energy is best written in terms of \( Q \):
\( \displaystyle U = \frac{Q^{2}}{2C} \;\Rightarrow\; U \propto \frac{1}{C} \)
The plates are identical, and the dielectric multiplies the capacitance by \( K = 4 \):
\( \displaystyle C_Y = K\,C_X = 4\,C_X \)
\( \displaystyle \frac{U_X}{U_Y} = \frac{C_Y}{C_X} = \frac{4}{1} \)
The battery voltage is not needed for the ratio.