Study with the several resources on Docsity
Earn points by helping other students or get them with a premium plan
Prepare for your exams
Study with the several resources on Docsity
Earn points to download
Earn points by helping other students or get them with a premium plan
The concept of capacitors, which are electronic devices that store energy in the electric field between a pair of conductors. It covers the different types of capacitors, dielectric materials, capacitance, calculating the electric field, potential difference, and capacitance. It also discusses charging and discharging a capacitor, and the discharge in a C-R circuit. equations and examples to illustrate the concepts.
Typology: Study notes
1 / 30
This page cannot be seen from the preview
Don't miss anything!
A capacitor is an electrical/electronic device that can store energy in the electric field between a pair of conductors (called "plates"). Figure 9.1: Kinds of capacitors The process of storing energy in the capacitor is known as "charging", and involves electric charges of equal magnitude, but opposite polarity, building up on each plate. Figure 9.1 shows different types of capacitors.
Capacitors are occasionally referred to as condensers. A wide variety of capacitors have been invented, including small electrolytic capacitors used in electronic circuits, basic parallel-plate capacitors, mechanical variable capacitors Dielectric materials Most types of capacitor include a dielectric spacer, which increases their capacitance. However, low capacitance devices are available with a vacuum between their plates, which allows extremely high voltage operation and low losses. Air filled variable capacitors are also commonly used in radio tuning circuits.
When any external connection is removed, the charge on the plates persists. The separated charges attract each other, and an electric field is present between the plates. The simplest practical capacitor consists of two wide, flat, parallel plates separated by a thin dielectric layer. Assuming that the plate size , where A is the area of the plates, is much greater than their separation d , the instantaneous electric field between the plates E ( t ) is identical at any location away from the edges. If the instantaneous charge on a plate, − q ( t ), is spread evenly, then
The voltage v ( t ) between the plates is given by
where z is the position between the plates. Capacitance What determines how much charge is on the plates of a capacitor for a given voltage? In other words what is the capacity of the device for storing charge at a particular value of?
In SI units, a capacitor has a capacitance of one farad when one coulomb of charge storage corresponds to one volt between its plates. Since the farad is a very large unit, capacitance is usually expressed in microfarads (μF), nanofarads (nF), or picofarads (pF). In general, capacitance is greater in devices with large plate areas, separated by small distances. When a dielectric is present between two charged plates, its molecules become polarized and reduce the internal electric field and hence the voltage. The capacitance is therefore strongly dependent on the quality of the dielectric.
Parallel Plate Capacitor Figure 9.3: Parallel Plate capacitor. Two parallel metallic plates of equal area A are separated by a distance d, as shown in Figure 9.3. One plate carries a charge Q, and the other carries a charge –Q. We consider how the geometry of these conductors influences the capacity of the combination to store charge.
Calculating the Electric Field The electric field E between the plates of a capacitor is related to the charge q on a plate by Gauss’ law: 9. Here q is the magnitude of the charge enclosed by a Gaussian surface, and is the net electric flux through the surface. In all the cases we consider here, the magnitude of E is E and the vectors E and d A are parallel Equation 9.4 reduces to 9. in which A is the area of that part of the Gaussian surface through which flux passes.
Calculating the Potential Difference The potential difference between the plates is related to the electric field E by 9. in which the integral is to be evaluated along any path that starts on one plate and ends on the other. For a path that follows an electric field line from the positive plate to the negative plate, the vectors E and d s will always point in the same direction, so that the dot product E .d s will be equal to the positive quantity Eds. Equation 9.6 in this case tells us that the quantity will always be negative. If we let , then 9. in which + and – remind us that our path of integration starts on the positive plate and ends on the negative plate.
Equation 9.9 means that the capacitance does indeed depend only on geometrical factors, namely, the plate area A and the plate separation d. Note also that C increases with increasing area A or decreasing separation d. Combinations of Capacitors Series circuits Series circuits are sometimes called current-coupled. The current that flows in a series circuit will flow through every component in the circuit. Therefore, all of the components in a series connection carry the same current.
The fig. shows two capacitor symbols connected in series. As a starting point, let's assume that these are two identical capacitors. The connection between them is assumed to have no resistance, and therefore no effect on the behavior of these two capacitors or any circuit in which they may be connected. This being the case, let's shorten the distance between the two capacitors to zero. This means that the connected plates of the two capacitors will actually touch, as shown
Since the capacitance of any capacitor is inversely proportional to the distance between the plates, we can express the total capacitance, CT, of any number of capacitors connected in series as: 9. For two capacitors in series, this can be written as: **9.
Parallel circuits If two or more components are connected in parallel as shown in Figure 9.7 they have the same potential difference (voltage) across their ends. The potential differences across the components are the same in magnitude, and they also have identical polarities. Hence, the same voltage is applicable to all circuit components connected in parallel. The total current I is the sum of the currents through the individual components. When this is done with capacitors, each capacitor charges to the same voltage, without regard to the behavior of the other capacitor.
From Q = CV , other relations for the energy stored in a capacitor W are 9. If C is measured in farad, Q in coulomb and V in volt, then the formulae will give the energy W in joules
Charging a Capacitor In Figure 9.8, an uncharged capacitor is shown connected to a four- position switch. With the switch in position 1 the circuit is open and no voltage is applied to the capacitor. Initially each plate of the capacitor is a neutral body and until a difference of potential is impressed across the capacitor, no electrostatic field can exist between the plates.
