Energy stored in the Capacitor & Energy Density

I am here now to discuss about the Energy stored in Capacitor

Capacitor

Energy Stored In a Capacitor :

Consider a parallel plate Capacitor it initially uncharged so that the initial potential difference across the plates is zero

Now imagine that the Capacitor is connected to a battery which develops a maximum charge "q" and a final potential across the plates is "V" 
Since the Capacitor is charged linearly the q-V graph is straight line passing through the origin

q-V Characteristics

Since the initial potential difference is zero, the average potential difference during the charging process

= (0+V)
= V/2

Energy Stored  U = V/2 ×q = 1/2 qV


The energy stored in the Capacitor can be expressed in alternate forms

•It is clear from the above expression that energy stored increases with increase of potential difference.



Energy Density :


The energy stored in the Capacitor can be considered as being stored in the Electric field created between the plates as the Capacitor is charged 

Consider a parallel plate Capacitor with  Area of Plate "A" and separation "d" 

Parallel plate Capacitor

Energy stored 
U = 1/2 CV^2

The energy stored per unit volume is called energy Density (u) since the volume of parallel plate is 'Ad'

Therefore energy Density ( i.e Electric field energy stored per unit volume ) in any region of space is directly proportional to the square of the Electric field Intensity in the region

Related Links :

Capacitor & Capacitance
Capacitance of parallel plate Capacitor

Capacitance of parallel plate Capacitor & Dielectric Constant & Dielectric Strength of Capacitor

Hello all here is another post about the Capacitor

Capacitor

Capacitance of a parallel plate Capacitor :

Parallel plate Capacitor
1) air as Dielectric 2) some other Dielectric medium

The figure shows a parallel plate air capacitor is given by 


Cair = ε0 A/d


Where  A is the area of each plate
          d is the plate separation


It is clear that capacitance of a parallel plate Capacitor is directly proportional to the area of plates and inversily proportional to plate separation

When space between plates completely filled with Dielectric the capacitance of capacitor is given by

Cm = εA/d
     = ε0εrA/d
     =εr Cair

Dielectric Constant of capacitor :

Capacitance of a parallel plate air Capacitor is Given by

Cair = ε0A/d


If the space between the plates completely filled with a Dielectric of relative Permittivity "εr" then the capacitance of capacitor is given by

Cm = εr Cair

Cm/Cair = εr


Dielectric Strength :

The maximum value of Electric field Intensity ( i.e potential gradient ) that can be applied to a Dielectric without it's Electric breakdown is called Dielectric strength of the Dielectric .

Related Topics :

Capacitor And Capacitance 

Electric field Intensity


Please Comment Below If You Have Any Suggestions Or Doubts

Capacitor And Capacitance

Capacitor :

Capacitor

A Capacitor is a device that is capable of storing charge. It essentially consists of two conducting surfaces separated by an insulating material.

The conducting surfaces are called plates of the capacitor and the insulating material is called Dielectric.
The most commonly used dielectrics are air,mica,paper etc

• A capacitor is generally named after the Dielectric used e.g air capacitor, mica capacitor, paper capacitor etc
• The capacitor may be in the form of parallel plates  (parallel plate capacitor ), concentric cylinders ( cylindrical capacitor ) or other arrangements

Capacitance :

Parallel plate capacitor connected to battery

The ability of a capacitor to share Charge is known as it's capacitance

Consider a parallel plate air capacitor connected to a battery. The  electrons from plate 'A' attracted by the battery and these electrons start pilling upon plate 'B' . This action is reffered as the charging of the capacitor because capacitor plates are being charged. It has been found experimentally that charge 'q' stored in a capacitor is directly proportional to the p.d (V) across the plates  i.e

q∝ V

q/V =Constant = C

The constant of proportionality C is called capacitance of capacitor . The unit of capacitance is farad

1 C/V = 1 farad

• By definition capacitance is always a positive quantity
• The p.d across the capacitor increases linearly with increase of Charge on the capacitor plate there fore the ratio q/V is constant for a given capacitor