# Capacitors

So far we have limited our study to resistive circuits. We will now consider two additional passive devices called the capacitor and the inductor (the inductor is discussed in detail in Chapter 10), which are quite different from the resistor in purpose, operation, and construction.
Unlike the resistor, both elements display their total characteristics only when a change in voltage or current is made in the circuit in which they exist. In addition, if we consider the ideal situation, they do not dissipate energy as does the resistor but store it in a form that can be returned to the circuit whenever required by the circuit design.
For this reason, capacitors and inductors are called storage elements.
Proper treatment of each requires that we devote this entire chapter to the capacitor and, as mentioned above, Chapter 10 to the inductor.

### What is Capacitor?

A capacitor is a passive element designed to store energy in its electric field. Besides resistors, capacitors are the most common electrical components. Capacitors are used extensively in electronics, communications, computers, and power systems. For example, they are used in the tuning circuits of radio receivers and as dynamic memory elements in computer systems. A capacitor is typically constructed as depicted in Fig.1(a).
(a)
(b)
Fig. 1: (a) A typical capacitor. (b) A capacitor with applied voltage v.
A capacitor consists of two conducting plates separated by an insulator (or dielectric).
In many practical applications, the plates may be aluminum foil while the dielectric may be air, ceramic, paper, or mica.
If a potential difference of V volts is applied across the two plates separated by a distance of d, the electric field strength between the plates is determined by $$E = {V \over d} \text{ (volts/meter, V/m)} \tag{ 1}$$ The uniformity of the flux distribution in Fig. 1(a) also indicates that the electric field strength is the same at any point between the two plates.
Many values of capacitance can be obtained for the same set of parallel plates by the addition of certain insulating materials between the plates.
Fig. 2: Effect of a dielectric on the field distribution between the plates of a capacitor: (a) alignment of dipoles in the dielectric; (b) electric field components between the plates of a capacitor with a dielectric present.
In Fig. 2(b), an insulating material has been placed between a set of parallel plates having a potential difference of V volts across them.
Since the material is an insulator, the electrons within the insulator are unable to leave the parent atom and travel to the positive plate. The positive components (protons) and negative components (electrons) of each atom do shift, however [as shown in Fig. 2(a)], to form dipoles. When the dipoles align themselves as shown in Fig. 2(b), the material is polarized. A close examination within this polarized material will indicate that the positive and negative components of adjoining dipoles are neutralizing the effects of each other. The layer of positive charge on one surface and the negative charge on the other are not neutralized, however, resulting in the establishment of an electric field within the insulator. The net electric field between the plates ($E_{resultant} = E_{air} - E_{dielectric}$) would therefore be reduced due to the insertion of the dielectric.
The purpose of the dielectric, therefore, is to create an electric field to oppose the electric field set up by free charges on the parallel plates. For this reason, the insulating material is referred to as a dielectric, di for "opposing" and electric for "electric field".
In either case with or without the dielectric, if the potential across the plates is kept constant and the distance between the plates is fixed, the net electric field within the plates must remain the same, as determined by the equation E= V/d.