(a) What is the total capacitance of the combination?

(b) What is the potential difference across each capacitor, if the combination is connected to a $$120\ volt$$ supply?

$$q_1=$$____

$$q_2=$$____

$$q_3=$$____

$$q_4=$$____

$$q_5=$$____

$$q_6=$$____

(i) Calculate the value of $$C$$.

(ii) Calculate the charge on each capacitor.

(iii) What will be the potential drop across each capacitor?

(b) Define the capacitance of capacitor. Derive and expression for the capacity at a parallel plate capacitor with a dielectric slab placed in between the plates of capacitor.

(a) charge before the dielectric was introduced.

(b) charge After the dielectric was introduced.

a. Strength of electric field inside the capacitor remains unchanged, if battery is disconnected before pulling the plates.

b. During the process, work is done by external force applied to pull the plates irrespective of whether the battery is disconnected or not.

c.Strain energy in the capacitor decreases if the battery remains connected

Derive an expression for equivalent capacitance of three capacitors when connected in series.

Derive an expression for equivalent capacitance of three capacitors when connected in parallel.

At which point (of the two) is the electric potential more and why?

If you were asked to design a capacitor in which small size and large capacitance were required, what would be the two most important factors in your design?

(a) the electrostatic self-energy of the ball;

(b) the ratio of the energy $$W_{1}$$ stored in the ball to the energy $$W_{2}$$ pervading the surrounding space.

(i) potential difference between the plates

(ii) electric field between the plates

(ii) energy stored in the capacitor

A particle with charge $$+q$$ is at the origin. A particle with charge $$-2q$$ is at $$x=2.00 \,m$$ on the x axis.

(a) For what finite value(s) of x is the electric field zero?

(b) For what finite value(s) of x is the electric potential zero?

The unit of voltage is $$JC^{-1}$$.

(a) What is the charge $$Q$$ on the ball? In figure (b), the ball has been sliced up and the slices spread out so that an equal amount of charge is at the hour positions on a circular clock face of radius $$R=8.00 \ cm$$. Now the electron is brought from an infinite distance to the center of the circle.

(b) With that addition of the electron to the system of $$12$$ charged particles, what is the change in the electric potential energy of the system?

$$C=\frac {C_1C_2C_3}{(C_1C_2+C_2C_3+C_3C_1)}$$

(a) What is the total capacitance of the combination?

(b) What is the potential difference across each capacitor, if the combination is connected to a 120 volt supply?

At a point due to a point charge, the values of electric field intensity and potential are 32 N$$C^{-1}$$ and 16 J $$C^{-1}$$ ,respectively. Calculate the

a. magnitude of the charge,and

b. distance of the charge from the point of observation.

The battery is disconnected and a dielectric slab is inserted to completely fill the space between the plates.

How will (i) its capacitance, (ii) electric field between the plates and (iii) energy stored in the capacitor be affected ? Justify your answer giving necessary mathematical expressions for each case.

(a) Identify an equipotential surface of the system.

(b) What is the direction of the electric field at every point on this surface?

(a) What is the total capacitance of the combination?

(b) What is the potential difference across each capacitor if the combination is connected to a $$120 V$$ supply?

Exercise:

In a parallel plate capacitor with air between the plates, each plate has an area of $$6\times 10^{-3} m^{2}$$ and the distance between the plates is 3 mm. Calculate the capacitance of the capacitor. If this capacitor is connected to a 100 V supply, what is the charge on each plate of the capacitor?

(a) While the voltage supply remained connected.

(b) After the supply was disconnected.

Find:

charge on each capacitor

equivalent capacitance of the network

energy stored in the network of capacitors

What are the possible change in potential ?consider both cases of a moving the proton .