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Capacitors are storage devices for electrical energy inside an electromagnetic field. It is a non-active or passive electrical component that has two ends or terminals. When both the parallel plates are connected in series to a battery, a parallel plate capacitor is formed, which may store some amount of electrical energy until the insulator or insulating capacity of the plate breaks down.
Terms related to capacitor
Dielectric materials: Dielectric materials are insulators with the ability to polarise in the direction of the electric field.
Energy stored in a capacitor:- The charge Q and voltage V between the plates of the capacitor is connected to the electrostatic potential energy stored in the capacitor.
Voltage in a capacitor: It is the difference of potential between two capacitor plates. A capacitor’s voltage rating refers to its maximum operating or working voltage.
Capacitance:- It refers to the volume of segregated electric charge that may be held on an ideal current source or group of conductors for each unit measurement of electrical potential.
In mathematical terms, it is given as C =∈0A/d.
Where
A = Area of the plate
d = distance between the plates.
∈0 is the permittivity in the vacuum.
Mathematical relation of Charge, Voltage, and a capacitor’s capacitance.
The flow of current through a capacitor is the time-dependent differentiation of the potential difference applied across the capacitor. To put it another way, a capacitor’s current is dependent on the rate at which the voltage across it varies.
As we know, the rate of flow of Charge is termed current. As a result, we may conclude that charge is directly related to voltage.
On introducing the capacitance to the equation, the proportionality sign changes to equality.
In mathematical terms, it is given as q = CV.
Where C = capacitance of the capacitor.
q = charge in the capacitor
V = The capacitor’s plate voltage.
Finding the dependency factor of the Charge
As we have already got the relation as q=CV, and we know that
C = ∈0A/d
Where A is the area of the plate,
d is the distance between parallel plates, and
∈0 is the permittivity in the vacuum.
So we can modify the relation of Charge by putting the capacitance values in it.
q=CV
q=∈0AV/d
Now, we obtained the fundamental relation here where The charge is primarily determined by three things. Keeping two constants can help us find the dependency of Charge on the third factor.
If area and voltage are constant.
q=∈0AV/d
q ∝1/d
The charge is negatively dependent on the separation between the conductive plates. That means the greater the space between them, the less is the Charge stored in the plates, and vice versa, when all other factors remain constant.
If distance and voltage are constant.
q=∈0AV/d
q ∝A
The Charge is directly dependent on the conductive plates’ surface area. That means the larger their area is, the more is the Charge stored in the plates, and vice versa, when all other factors remain constant.
If distance and area are constant.
q=∈0AV/d
q ∝V
The Charge is directly dependent on the potential difference applied between the plates. That means the more the voltage is applied between them, the more the Charge gets accumulated on the plates, and vice versa, when all other factors remain constant.
Conclusion
The capacitor is a device designed to hold Charge by applying a voltage difference across it. It is made up of two plates across which a battery is applied to create a field that can produce Charge. There are several factors on which the Charge of the capacitor is dependent.
Summing up all the factors, the Charge depends upon the gap or space between the plates, the surface area of the conductive plates, and the voltage applied across the plates. It is negatively dependent upon the first factor but positively dependent upon the other two factors.
