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Understanding Physics Topics is essential for solving complex problems in many fields, including engineering and medicine.
What are the Factors affecting the Capacitance of a Capacitor?
Capacitor: A capacitor (originally known as condenser) is an arrangement by which the capacitance of a conductor can be increased.
It is used for storage of charge. Hence, a capacitor can alter-natively be defined as an arrangement which can store a certain amount of charge.
Usually, a capacitor uses the principle of artificially increasing the capacitance of an insulated charged conductor by bringing another earthed conductor near it.
Construction of capacitor: A capacitor is basically an arrangement of an insulated conductor and an earthed conduc-tor held close to each other and separated by air or a non-con-ducting (dielectric) medium. The shape of the two conductors is usually the same, e.g., in case of a parallel plate capacitor, two parallel metal plates are placed close to each other. Again, a spherical capacitor consists of two concentric spheres and a cylindrical capacitor of two co-axial cylinders.
Working principle of capacitor: An insulated metal plate A is connected to an electrical machine [Fig.(a)]. Suppose, the potential of the plate is + V when it is fully charged. If C be the capacitance of the plate, the charge on the plate will be, Q = CV.
Now if a similar plate B is placed in front of the plate A, then due to induction, a negative charge is induced on the inner surface of B and a positive charge on its outer surface. Induced negative charge, being nearer, lowers the positive potential of the plate A . Thus, the capacitance of the plate A increases a little (since C = \(\frac{Q}{V}\)). Hence the plate A takes a slight additional charge from the electrical machine and raises its potential again to V.
Now if B is earthed, positive charge on the far side of it moves to the earth [Fig.(b)] and influence of positive charges being absent, the potential of A falls further. So the capacitance of A increases further and consequently it will now be able to receive a greater amount of charge from the machine.
So in this way, the capacitance of an insulated charged conduc-tor can be increased with the help of another earthed conductor, placed in its vicinity.
Factors affecting the capacitance of a capacitor:
- Overlapping area of the plates: Greater the surface area of the plates, greater will be its capacitance. Capacitance decreases with the decrease of overlapping area.
- Distance between the two conducting plates: Capacitance increases with the decrease of this distance and vice versa.
- Nature of the intervening medium between the two con-ducting plates: Instead of air, if the intervening space of the two plates is filled up with an insulator, e.g., paraffin, glass, paper, etc., the capacitance of a capacitor increases.
Uses of capacitor: Extensive uses of the capacitors are found in different electrical circuits. In case of different circuits in ac, capacitor is almost an indispensable part. Capacitors are used in electronic instruments, radio, television, telephone, flash circuit of a camera etc.
Discussions:
i) Charge of a capacitor: Charge of a capacitor means the magnitude of charge on any one of its plates. If one plate possesses a charge + Q , then the other plate will contain a charge -Q. So total charge = +Q + (-Q) = 0. Here, Q is called the charge of a capacitor, it is not the total charge.
ii) Ideal capacitor: If a capacitor is connected to a source of high potential, it is charged to that potential. The capacitor is called an ideal one, if it is not discharged automatically even if the source of potential is removed. It preserves its acquired charge without any leakage.
iii) Maximum limit of the potential of a capacitor: A capaci-tor cannot be charged to any high potential at will. If the value of the potential exceeds a certain maximum limit, the intervening medium loses its insulating properties. Consequently, electric discharge takes place between the capacitor and the intervening medium.
iv) Any charged conductor is a capacitor: Any charged conductor may be considered as a capacitor. The floor or the walls of the room acts as the earthed conductor in this case.
v) Circuit symbol of capacitor: Two parallel lines of same size in an electrical circuit diagram, represents a capacitor
[Fig.(a)]. Symbol of a variable capacitor has been shown in Fig.(b)]
Charging and discharging of a capacitor: when a battery is connected to a series resistor and capacitor, charges begin to accumulate on the capacitor. This is called charging of a capacitor. After removal of the battery, the capacitor loses its accumulated charge through the resistor gradually. This is called discharging of a capacitor.
The two plates A and B of a capacitor are connected to a bat-tery of electromotive force E through a resistor [Fig.]. Elec-trons from the negative pole of the battery move to the plate B. Simultaneously, a flow of electrons starts from the plate A to the positive pole of the battery. This produces a charging current. As negative charges on the plate B and positive charges on the plate A keep on accumulating, the potential difference between the two plates increases. So the plates act as a cell and conse-quently, a tendency of electron flow is established in the direc-tion opposite to that of the initial electron flow.
As a result, the charging current decreases. When the potential difference between the two plates A and B becomes equal to the emf of the battery, the charging current ceases to flow. Then it is said that the capacitor has become fully charged. So at the start, the charging current is maximum and afterwards it gradually decreases. When the capacitor is fully charged, the charging cur-rent becomes zero [Fig.].
After removal of the battery from the circuit, i.e., during dis-charging electrons from the plate B flow to the plate A and begin to neutralise the positive charge of the plate A . Thus again a current flows in the circuit. This is called discharging current and its direction is opposite to that of the charging current.
After a while all the electrons of the plate B. neutralise all the positive charges of the plate A . Then the discharging current becomes zero and the capacitor is said to be completely discharged. So at the start, discharging current is maximum and it decreases gradually and becomes zero when the capacitor is completely discharged [Fig.].
In fact, no capacitor is an ideal one. A fully charged capacitor loses its charge in course of time even if the two plates of it are not connected by a conducting wire. Finally, the capacitor becomes completely discharged. Of course, in this case, the dis-charging action continues for a long time.
Potential and Capacitance of a Capacitor
Potential Of a capacitor: The potential difference between the two conducting plates of a capacitor is called the potential of a capacitor. Generally the potential of a capacitor means the potential attained by the insulated plate of the capacitor due to the charge given to it, the grounded plate of the capacitor being at zero potential.
Capacitance of a capacitor: The capacitance of a capacitor means the capacitance of the insulated conducting plate of the capacitor. So it may be defined as the amount of charge which must be given to the insulated plate to raise its potential by unity. If a charge Q raises its potential by V, its capacitance, C = \(\frac{Q}{V}\).
Therefore, the capacitance of a capacitor may be defined as the ratio of the magnitude of charge on any one of the two plates to the difference of potential between them, i.e.,
capacitance of a capacitor
The capacitance of a capacitor is assigned a value of 1 farad if 1 coulomb of charge is required to maintain a potential difference of 1 V between the two conductors or plates of the capacitor.
Here capacitance is always a positive quantity and it does not depend on the nature of charge and potential. The capacitance of a conductor and that of a capacitor are expressed in the same unit.
Usually, a capacitor is rated, bearing the mark of the magnitude of its capacitance and the maximum potential difference that can be applied safely between its two plates. A capacitor rated 0.04µF-220 V means that its capacitance is 0.04µF and the maximum potential difference to be applied between its two plates is 220 V. If it is used in a potential difference higher than 220 V, it may get damaged.