Combination of Capacitors

Three capacitors of capacitance `C_1 = 3muf` , `C_2 = 6muf` , `C_3 = 10muf` , are connected to a 10V battery as shown in figure 3 below : 

Calculate :

(a) Equivalent capacitance.

(b) Electrostatic potential energy stored in the system 

In the circuit shown in figure, initially K₁ is closed and K₂ is open. What are the charges on each capacitors.

Then K₁ was opened and K₂ was closed (order is important), What will be the charge on each capacitor now? [C = 1µF]

A capacitor 'C', a variable resistor 'R' and a bulb 'B' are connected in series to the ac mains in circuit as shown. The bulb glows with some brightness. How will the glow of the bulb change if (i) a dielectric slab is introduced between the plates of the capacitor, keeping resistance R to be the same; (ii) the resistance R is increased keeping the same capacitance?

A capacitor of capacitance 5⋅00 µF is charged to 24⋅0 V and another capacitor of capacitance 6⋅0 µF is charged to 12⋅0 V. (a) Find the energy stored in each capacitor. (b) The positive plate of the first capacitor is now connected to the negative plate of the second and vice versa. Find the new charges on the capacitors. (c) Find the loss of electrostatic energy during the process. (d) Where does this energy go?

Deduce an expression for equivalent capacitance C when three capacitors C₁, C₂ and C₃ connected in parallel.

An ac circuit consists of a series combination of circuit elements X and Y. The current is ahead of the voltage in phase by `pi/4`. If element X is a pure resistor of 100 Ω,

(a) name the circuit element Y.

(b) calculate the rms value of current, if rms of voltage is 141 V.

(c) what will happen if the ac source is replaced by a dc source

The plates of a capacitor are 2⋅00 cm apart. An electron-proton pair is released somewhere in the gap between the plates and it is found that the proton reaches the negative plate at the same time as the electron reaches the positive plate. At what distance from the negative plate was the pair released?

An ac circuit consists of a series combination of circuit elements X and Y. The current is ahead of the voltage  in phase by `pi /4` . If element X is a pure resistor of 100Ω ,

(a)  name the circuit element Y.
(b)  calculate the rms value of current, if rms value of voltage is  141V.
(c)  what will happen if the ac source is replaced by a dc source ?