Two parallel plate capacitors X and Y have the same area of plates and same separation between them. X has air between the plates while Y contains a dielectric medium of ϵr = 4.
(i) Calculate capacitance of each capacitor if equivalent capacitance of the combination is 4 μF.
(ii) Calculate the potential difference between the plates of X and Y.
(iii) Estimate the ratio of electrostatic energy stored in X and Y.
(i)
The value of 
and 
Given
The area and separation between the two plates/ capacitor X and Y are same, the dielectric medium of 
. The equivalent capacitance of the combination is 
. The circuit diagram 15.1 is given as
Formula Used
To find the capacitance of the capacitor we use the formula of generalised equation of capacitance as
where
is the permittivity of the free space, 
is the relative permittivity, A is the area of the plate, d is the distance between the plates.
Therefore, the capacitance of each capacitor if the equivalent capacitor is
Capacitance of plate Y is
Capacitance of plate X is
Therefore, the capacitance equivalent is
Therefore, after calculation the value of 
and 
(ii) The potential difference is 
Given
The area and separation between the two plates/ capacitor X and Y are same, the dielectric medium of
. The equivalent capacitance of the combination is 
. The circuit diagram 15.1 is given as
Formula Used
The formula used is the capacitance formula which is the ratio of the charge by voltage across the plate.
where
C is the capacitance, V is the voltage, Q is the charge supplied.
The 
of the circuit is 
The potential difference between the plates is
After solving we get the value of the voltages as
(iii)
The ratio of the electrostatic energy stored is 2:3
Given
The area and separation between the two plates/ capacitor X and Y are same, the dielectric medium of 
. The equivalent capacitance of the combination is 
. The circuit diagram 15.1 is given as
Formula Used
The ratio of the capacitance is equivalent to the ratio of the energy of the plates which is
where
C is the capacitance, E is the energy, Q is the charge supplied.
The ratio of the energy on the plate is
Therefore, the ratio of the electrostatic energy stored is 2:3
Couldn't generate an explanation.
Generated by AI. May contain inaccuracies — always verify with your textbook.
