Important Problems on Capacitors and capacitance for JEE Main And Advanced

Question 1
A parallel plate air capacitors has plate area 0.2 m2 and has separation distance 5.5 mm. Find
(a) Its capacitance when capacitor is charged to a potential difference of 500 volts
(b) Its charge
(c) Energy stored in it
(d) Force of attraction between the plates

Question 2
Consider a system of capacitors where two parallel plate air capacitors each of capacitance C are connected in series to a battery of EMF ξ. Now one of the capacitor is filled uniformly with a dielectric of dielectric constant K. What would happen to electric field strength of that capacitor and what would be the change in electric field strength?  Calculate the amount of charge that flows through the battery?

Question 3
A spherical capacitor has charges + Q and - Q on its inner and outer conductors. Find the electric potential energy stored in the capacitor?

Question 4
Find the capacitance of an isolated spherical conductor of radius r1 surrounded by an adjacent concentric layer of dielectric with dielectric constant K and outside radius r2.

Question 5
In a parallel plate air capacitor having plate separation 0.05mm, an electric field of 4 x 104 V/m is established between the plates. After the removal of the battery a metal plate of thickness t=0.02 mm is inserted between the plates of the capacitor. Find
1. Potential difference across capacitor before the introduction of metal plates.
2. Potential difference across capacitor after the introduction of metal plates.
3. Potential difference across capacitor if dielectric slab with dielectric constant K=3 and same thickness were inserted in place of metal plate.

Question 6
Find the capacitance of four parallel plates each of area Am2 and separated by a distance d1, d2, and d3 . The space between them is filled with dielectrics of relative permittivity ε1, ε2 and ε3 . Permittivity of free space is ε0.

Question 7
Consider the figure given below

1. Find the equivalent capacitance between A and B
2. Find the potential difference between 3μF capacitor
3. Find the amount of charge on 2μF capacitor
4. Find the energy stored on 12μF capacitor

Question 8
Two parallel plate condensers A and B having capacities 2 μF and 10 μF are charged separately to the same potential of 200V. Now, positive plate of  A is connected to negative plate of B and the negative plate of A is connected to positive plate of B.
1. Calculate the equivalent capacitance and the common voltage of combination A-B.
2. Find the loss in electrical energy in each condenser.

Question 9
The plates of a parallel plate capacitor are separated by a dielectric whose relativity permittivity varies according to following relation

Find the capacitance of the capacitor.

Question 10
Find the charge on 5 μ F capacitor in the circuit given below

Question 11
If 20 drops of same size, each having the same charge, coalesce to form a bigger drop. How will the following vary with respect to single small drop?
(i)Total charge on bigger drop
(ii) Potential on the bigger drop
(iii) The capacitance on the bigger drop
Consider the drops to have spherical symmetry.

Question 12
A Parallel Plate capacitor has following dimensions
Distance between the plates=10 cm
Area of Plate=2 m2
Charge on each plate=$8.85 \times 10^{-10}$ C
Calculate following
(a)Electric Field outside the plates
(b)Electric Field Between the plates
(c)Capacitance of the capacitor
(d)Energy stored in the capacitor
$\epsilon _0=8.854 \times 10^{-12} \ C^2N^{-1}m^{-2}$