Is Capacitance Independent of Charge and Potential?

A capacitor is one of the three fundamental components of the electronics and is used to store energy in circuits. The ability of a capacitor to store energy is called capacitance. A typical representation of the parallel plate capacitor is shown in Fig. 1

Fig. 1 

Suppose there is a parallel plate capacitor that is connected across a voltage source V, this will cause positive and negative charges (Q) to be accumulated on the plates. The charge stored on the plates is directly proportional to the applied voltages.

 Q α V

Where

Q = Charge

V = Voltage

 Q = CV

Where C is capacitance and it is proportionality constant.

 C = Q / V

The capacitance of a capacitor can also be defined as the ration of charge on the capacitor plates (Q) to the voltage (V) between them. The unit of the capacitance is Farad; capacitance of the capacitor will be one farad if one coulomb of charge causes a potential difference of one volt across the capacitor plates. By changing the Q or V capacitance of a capacitor cannot be changed since these two terms are directly proportional and the resultant capacitance will remain the same.

The capacitance of a capacitor is actually determined by the physical parameters of the capacitor along with the properties of the dielectric material that is used during the manufacturing of the capacitor. The capacitance of a capacitor is directly proportional to the area of the plates that are forming the capacitor

C α A

Where

C = Capacitance

A = Area

Also, capacitance is inversely proportional to the distance between the plates of the capacitor

C α 1/d

Where

d = distance

So now

C α A/d

As mentioned earlier capacitance depends on the physical parameters like area (A) and distance (d) it also depends on the property of the dielectric material. It is the permittivity (ɛ) of the dielectric material that plays the role as the energy stored in the capacitor is in the form of electric field and permittivity is the ability of the dielectric material to get polarized due to the application of the electric field. Permittivity is a constant for every material [2].

Thus,

C = ɛ A/ d

Now there is no V or Q in the equation for the capacitance. Therefore it can be told that the capacitance of a capacitor does not depend on the charge or potential, it depends on the physical parameters of the capacitor and material used as a dielectric.