Charging and Discharging of capacitor:
In case of charging, when a capacitor charged by a battery of V volt, a high resistance is connected in series with the capacitor, as capacitor initially act as short circuit. After that the voltage gradually increases across capacitor and stops when it equals to the supply voltage V, that means charging current are high at initial then it lower down as voltage grows up.
In case of discharging, when source voltage removed, the capacitor starts discharging. It is seen that the discharging current are maximum at initial like charging current and then it decreases but still discharging till it become fully uncharged.
Time constant:
After charging, if we disconnect the capacitor, it will not hold the charge for infinite time. Due to internal leakage it slowly discharges through its dielectric. The time taken to discharge to 0.632 of its initial maximum voltage is known as time constant.
It is defined as, t = CR.

Capacitor in series connection:
If we connect some capacitor in series across a voltage source, the equivalent capacitance value will be lower than any single capacitor capacitance value of that series connection.
Suppose three capacitor C1, C2 and C3 are connected across a voltage source V.
The voltage drop across capacitors are VC1, VC2 and VC3.
So, V = VC1+ VC2 + VC3.
If Q coulomb be the charge, then Q = CV or, V=Q/C.
V C3=Q/C3.
As per equation, we can write,
Q/C = Q/C1+Q/C2+Q/C3
Or, 1/C = 1/C1+1/C2+1/C3.
If there is n number of capacitor connected in series, then,
1/C = 1/C1+1/C2+1/C3+………..+1/Cn.

Now, if we put the value of capacitance in above equation, just like C1=2µF, C2=3µF, C3=4µF,
So, 1/C=1/2+1/3+1/4.
Or, C=0.925 µF.
Lower than any connected capacitance value.

Capacitor in parallel connection:

If we want to increase the capacitance value, we should connect two or more capacitors in parallel combination.
In this case, capacitor C1, C2, C3 are connected in parallel across a voltage source, V volt.
In parallel circuit, the supply voltage is same in each circuit across the each capacitor, i.e, V=VC1= VC2= VC3.
The total charge of the parallel combination is divided by each capacitor.
So, Q =QC1+QC2+ QC3.
As, Q=CV, CV=C1V+ C2+ C3V,
Or, C= C1+C2+C3.
In case of n number capacitor, C = C1+C2+C3+….+Cn.
If we put a value in above equation, if C1=2µF, C2=3µF, C3=4µF,
Then, C =2+3+4=9µF.

Types of capacitor:

There are various types of capacitors are available, the major types are ceramic capacitor. In these types of capacitor, various types of ceramic dielectrics are used. The common compounds are titanium dioxide, strontium titanate. It is used in radio and audio frequency application.

Electrolytic capacitor: These types of capacitors are polarized, that is positive and negative plate is marked. If we connect in reverse, the dielectric may breakdown. In this type of capacitor an electrolyte is used for higher capacitance value. The plate is constructed by conducting aluminium foil and the paper spacer electrolyte placed between the plates. It is used in low frequency application like power supply.

Mica capacitor: Mica is the dielectric medium of these types of capacitor. Here thin sheet of silver foil placed between the mica insulation. Several layers are used for required capacitance, uses in RF application and filter circuit.

Tantalum capacitor: This is also polarized capacitor with very high capacitance value. This types of capacitor are very reliable, has wide temperature range, good frequency characteristics but it cannot withstand reverse voltage and it is more expensive too.

Polyester film capacitor: Polyester has high dielectric strength and use as dielectric medium. Here metal and polyester layers are used to increase capacitance value. These types of capacitors are cheap.

Air capacitor: Here air is used as dielectric medium. It is made by two conducting plates, separated by air.
Glass capacitor: As name implies, glass used as dielectric medium. It has low temperature co efficient and ability for withstanding high operating temperature. Here aluminium used as electrode. It is used in high power amplifier.

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