# A capacitor is a system of two conductors separated

## Case Study Chapter 2Electrostatic Potential and Capacitance :

A capacitor is a system of two conductors separated by an insulator. The two conductors have equal and opposite charges with a potential difference between them. The capacitance of a capacitor depends on the geometrical configuration(shape, size and separation) of the system and also on the nature of the insulator separating the two conductors. They are used to store charges. Like resistors capacitors can be arranged in series or parallel or a combination of both to obtain desired value of capacitance.                                    [CBSE  2023]

(i) Find the equivalent capacitance between points A and B in the given diagram.                     (1)

(ii) A dielectric slab is inserted between the plates of a parallel plate capacitor. The electric field between the plates decreases, Explain.                      (1)

(iii) A capacitor A of capacitance C having charge Q is connected across another uncharged capacitor B of capacitance 2C. Find an expression for (a)  The potential difference across the combination and (b) The charge lost  by capacitor A.                                 (2)

OR

(iii) Two slabs of dielectric constants 2K and K fill the space between the plates of a parallel plate capacitor of plate area A and plate separation as shown in figure. Find an expression for capacitance of the system.                      (2)

### Solution :

(i)

Total capacitance between AB = 2C

(ii) When a dielectric is inserted between the plates of a capacitor, the electric field decrease. This is due to polarisation of the charge within the dielectric, which results in induced surface charges. Capacitor is greater by a factor K, where K is the dielectric constant of the material.

(iii) (a) Potential,

(b) Charge lost by capacitor A = Q/3.

OR

(iii) We know that,

Now, the effective capacitance for series combination,