Parallel plate capacitor
In this topic we will discuss about capacitance and its principle ,and expression for the capacitance of parallel plate capacitor .
Capacitor and its principle – It is an arrangement in which large amount of electric charge can be stored and hence develop large potential difference in small space. A capacitor consists of a system of two conductors separated by an insulating medium. Often the two conductors are charged by connecting them to the two terminals of a battery. Or we can say that the capacitance of an insulated conductor is increased considerably by bringing near it an uncharged conductor connected to earth.
If the conductors are plane , the capacitor is called a parallel plate capacitor , when the conductor is spherical called spherical conductor , and if the conductor is cylindrical then the capacitor is called cylindrical capacitor .
Parallel plate capacitor – A parallel plate capacitor consists of two thin conducting plates each of plate area ‘A’ and separated by distance ‘d’ . One of the plate is insulated and the other plate is earthed . When charge Q is given to one plate then the charge -Q is induced on the near face of the second plate and +Q on the farther face of the second plate , and +Q is flows to the earth .
The surface charge density of the first plate is +σ = Q/A
And on the other plate is -σ = -Q/A .
So electric field between the plates is E = σ/ϵ0 = Q/Aϵ0 ;
Potential difference between the plates is V = E.d = Qd/Aϵ0
Hence capacity of the capacitance will be C = Q/V = Q/( Qd/Aϵ0 ) = Aϵ0 / d i.e . the capacitance of parallel plate capacitor is independent of the charge and potential .