Q. 15

Two parallel plat

Answer :

(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


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