After this comes the concept of capacitor !
What is a capacitor; It is a device to store charge. Now why do we require to store ? Basically we want to use charge as and when required. So we devised a capacitor.
Let us understand the principle of capacitor :
In figure 1 there is a plane metallic sheet, and some charge is placed on it. Now if we see, for the first charge I don’t have to do any work as there is no repulsive force, BUT for the second charge we will perform some work as we have some repulsive force, similarly as we increase the charge we have to do more and more work. Now work done per unit charge, is defined as potential.
In other words as the charge on conductor increases its potential increases.
Let us take 2 plates and charge them Refer to Figure 2 to Figure 4. When we give charge to plate A without giving any charge to plate B. now as B is conductor kept near a charged conductor it induces charge as shown in Figure 1. If now plate B is connected to ground all the charge +ve of plate B is goes to ground & only -ve charge stays on it as shown in Figure 2.
Now as the ground connection is removed the charges redistribute as shown in Figure 3. Now both +ve & -ve charges are attracting each other and thus are stored very closely in same conductor. As charge is introduced to conductor its potential increases we may say that Q is proportional to V voltage thus Q ∝ V or Q = CV
It can be stated that capacitance is ratio of potential to charge for a conductor. And its unit is Farad. So as discussed mathematically 1 Farad is said to be the capacity of capacitor or conductor if 1 Coulomb of charge raises the potential on conductor by 1 Volt.
To find the capacitance we do the same i.e. first charge the conductor & then study its potential in terms of charge, then we divide the two and get the capacitance.
Capacitors are classified as the shape of conductors forming it
(i) parallel plate capacitor.
(ii) spherical capacitor
(iii) cylindrical capacitor etc.
OR on the basis of material filled in between the plates i. e.
(i) Electrolytic
(ii) Ceramic
(iii) Paper
(iv) Mica
Most common capacitor is parallel plate capacitor.
Let us try to get the value of capacitance of parallel capacitor, if we take the capacitor with plate area ‘A’ and distance between the plates as ‘d’. Now if the charge Q is given the electric field inside is given as E = σ/ε0 Also we know that E = V/d or in other words V = E.d
Knowing the value of electric field in terms the charge on capacitor. We get a relation between charge Q and potential V.
WE DIVIDE CHARGE Q by POTENTIAL V and we get the capacitance.
We see the capacitance is depending on Plate area A, distance between ‘d’ and the permittivity. And also we see that to increase the capacitance either the area is to be increased or the distance between the plates is to be decreased. Let us now analyse that, what happens when area is increased. As we increase the Area the net size of capacitor increase, then it becomes difficult to put it in desired circuit. Next as we decrease the distance there is chance of charge leaking and hence the basic purpose is being defeated. Thus we cans say the we have practical limitations in increasing the area and decreasing the distance between plates.
Now what is the option !
We use more than one capacitor, But how to add them !
We are having two options Either attach them in SERIES or attach them in PARALLEL.
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Now let us analyse !
In series connection Charge Q is constant, but potential is added, while in parallel Voltage V is constant and charges Q are added.
In series the NET capacitance is less that the least and capacitors are added as
Ceq–1 = C1–1 + C2–1
While in parallel the net capacitance is larger than the largest, and Ceq = C1 + C2
Then we try to find the energy of capacitor while charging. We are having three different formulas as energy of capacitor.
½CV² = ½ QV = Q²/2C