Capacitance And capacitor

1. Introduction

A capacitor (formerly known as condenser) is a device that can store electronic charge and energy.
All capacitors consists of a combination of two conductors separated by an insulator.
The insulator is called dielectric which could be oil, air or paper and many more such materials are there wich can act as a dielectric medium between conducting plates of a capacitor.
Figure 1 below shows the symbol used to represent a capacitor.
Now plates of the capacitor are connected to the terminals of a battery, shown below in figure 2, in order to charge it's conducting plates.
As soon as capacitor is connected to the battery , charge is transferred from one conductor to another.
Plate connected to positive terminal of the battery becomes positively charged with charge +Q in it and plate connected to negative terminal of the battery becomes negatively charged with charge -Q on it i.e. both plates have equal amount of opposite charge .
Once the capacitor is fully charged potential difference between the conductors due to their equal and opposite charges becomes equal to the potential difference between the battery terminals.
For a given capacitor Q∝V and the ratio Q/V is constant for a capacitor.
Thus,
Q=CV (1)
where the proportionality constant C is called the capacitance of the capacitor.
Capacitance of any capacitor depends on shape , size and geometrical arrangement of the conductors.
When Q is in coulombs (C) and V is in volts(V) then the S.I. unit of capacitance is in farads(F) where
1F=1 coulomb/volt
One farad is the capacitance of very large capacitor and it's sub-multiples such as microfarad(1μF=10^-6) or picofarad(1pF=10^-12) are generally used for practical applications.

2. Calculation of capacitance

For calculating capacitance of a capacitor first we need to find the potential difference between it's two conducting plates having charge +Q and -Q.
For simple arrangements of conductors like two equivalent parallel plates kept at distance d apart or two concentric conducting spheres etc., potential difference can be found first by calculating electric field from gauss's law or by Coulomb's law.
After calculating electric field , potential difference can be found by integrating electric field using the relation
V_a-V_b=∫E.dr
where the limits of integration goes from a to b.
Once we know the potential difference between two conductors of the capacitor , it's capacitance can be calculated from the relation
C=Q/V (2)
Calculation of capacitance of some simple arrangements would be illustrated in following few articles.