Capacitance and Capacitors

Learning Goals - The nature of capacitors, and how to calculate their ability to store charge. How to analyze capacitors connected in a network. How to calculate the amount of energy stored in a capacitor. What dielectrics are, and how they make capacitors more effective.

The Nature of CapacitanceCapacitance is a measure of the ability of a component to store charge.

A capacitor is a device specially designed to have a certain amount of capacitance.

The parallel-plate capacitor, shows two parallel surfaces, or plates, made of conducting material and separated by an insulator.

The insulator between the plates is called the dielectric.

There are many different kinds of capacitors, and they are categorized by the type of dielectric material used between the conducting plates.

Although any good insulator can serve as a dielectric, each type has characteristics that make it more suitable for particular applications.

Electrical capacitanceDefined as the amount of charge per volt that an object can hold

Some Capacitorsinsulatorconductor

Capacitance : DefinitionTake two chunks of conductorSeparated by insulatorApply a potential V between themCharge will appear on the conductors, with Q+ = +CV on the higher-potential and Q- = -CV on the lower potential conductorC depends upon both the geometry and the nature of the material that is the insulatorQ+ = +CVQ- = -CV

A Capacitor StoresCHARGEVApply a Potential Difference VAnd a charge Q is found on theplatesQ

Anything can be a capacitor

The capacitance is defined as Q/V, but it is also solely dependent on the geometry of the capacitor. There should be an equation for the capacitance that is based only on the physical dimensions of the capacitor.

The capacitance is measured in farads (F) after Michael Faraday

*Michael Faraday (1971-1867)

* CapacitorsA capacitor consists of two conducting plates separated by an insulator (or dielectric).

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A capacitor consists of two conducting plates separated by an insulator (Dielectric).

The amount of charge stored, represented by q, is directly proportional to the applied voltage V.

A is the surface area of each plate, d is the distance between the plates.

Capacitors are used to block dc, pass ac, shift phase, store energy, start motors, and suppress noise.

*Three factors affecting the value of capacitance:

Area: the larger the area, the greater the capacitance.

Spacing between the plates: the smaller the spacing, the greater the capacitance.

Material permittivity: the higher the permittivity, the greater the capacitance.

DielectricAdding a material to the space between the plates changes the capacitance of the capacitor

Table 20-1Dielectric Constants

SubstanceDielectric constant, k

Water80.4Neoprene rubber6.7Pyrex glass5.6Mica5.4Paper3.7Mylar3.1Teflon2.1Air1.00059Vacuum1

**V0V Capacitors with dielectricsA dielectrics is an insulating material (rubber, glass, etc.)Consider an insolated, charged capacitor

Notice that the potential difference decreases (k = V0/V)Since charge stayed the same (Q=Q0) capacitance increases

dielectric constant: k = C/C0 Dielectric constant is a material property

Insert a dielectric

**Capacitors with dielectrics Capacitance is multiplied by a factor k when the dielectric fills the region between the plates completelyE.g., for a parallel-plate capacitor

The capacitance is limited from above by the electric discharge that can occur through the dielectric material separating the plates

In other words, there exists a maximum of the electric field, sometimes called dielectric strength, that can be produced in the dielectric before it breaks down

Effect of Dielectric Material on CapacitanceThe dielectric material in a capacitor is an insulator, electrons are strongly bound to their parent atoms and are not free to travel under the influence of an electric field.

When an electric field is established in the dielectric by charging the capacitor plates.

*Types of Capacitors(a) Polyester capacitor, (b) Ceramic capacitor, (c) Electrolytic capacitor

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Variable capacitors

Ch06 Capacitors and Inductors*Voltage Limit on a CapacitorSince q=CV, the plate charge increases as the voltage increases. The electric field intensity between two plates increases.

If the voltage across the capacitor is so large that the field intensity is large enough to break down the insulation of the dielectric, the capacitor is out of work. Hence, every practical capacitor has a maximum limit on its operating voltage.

Q1a).Calculate the charge stored on a 3- PF capacitor with 20V across it. b). Find the energy stored in the capacitor.

a). Q = CV Q = 3 x 10-12 x 20 = 60 PC b). The energy stored is, w = CV2 = x 3x10-12 x 400 = 600 PJ

Q2. A 6-V source is required to store 24 micro Coulomb of charge on a certain capacitor.

a). What is the capacitance of the capacitor?

b). How much charge is stored on the capacitor when a 9-V source is connected across it?

c). What is the voltage across the capacitor when 16 micro coulomb is stored on it?Solution:

a). C = Q/V = (24 x 10-6 )/6 = 4 x 10 -6 F

b). Q = CV = (4 x 10 -6 F) x (9V) = 36 x 10-6 C

c). V = Q/C = 16 x 10 -6 / 4 x 10 -6 F = 4 V.

Any two conductors insulated from one another form a CAPACITOR. A "charged" capacitor can store charge. When a capacitor is being charged, negative charge is removed from one side of the capacitor and placed onto the other, leaving one side with a negative charge (-q) and the other side with a positive charge (+q).

** Combinations of capacitorsIt is very often that more than one capacitor is used in an electric circuitWe would have to learn how to compute the equivalent capacitance of certain combinations of capacitorsC1C2C3

Two Types of ConnectionsSERIES

PARALLEL

A charged parallel plate capacitor.Q = C V where C = eo A / d for a parallel plate capacitor, where eo is the permittivity of the insulating material (dielectric) between plates. Recall that we used Gauss's Law to calculate the electric field (E) between the plates of a charged capacitor: E = s / eo where there is a vacuum between the plates. Vab = E d, so E = Vab /dThe unit of capacitance is called the Farad (F).

**Series combinationAnalogous formula is true for any number of capacitors,

It follows that the equivalent capacitance of a series combination of capacitors is always less than any of the individual capacitance in the combination(series combination)

*Series CapacitorsThe equivalent capacitance of series-connected capacitors is the reciprocal of the sum of the reciprocals of the individual capacitances.

Capacitors in seriesAdding capacitors in series, Vtot = V1 + V2, so The charge on each capacitor must be the same when they are connected in series Why?

**Capacitors consist of two chunks of conductor, separated by a volume of dielectric (insulator). Any two such chunks form a capacitor. Here are some examples.*Self-explanatory, I think. By geometry, we mean the shape and separation of the two chunks of conductor. The material material that is the insulator means that two identical capacitors with (say) ceramic between the plates of one and air netween the plates of the other will have different capacitances.***The amount of charge that can be placed on a capacitor is proportional to the voltage pushing the charge onto the positive plate. The larger the potential difference (voltage) between the plates, the larger the charge on the plates. Q = C V the constant of proportionality is called the "capacitance" and is proportional to the area (A) of one of the plates and inversely proportional to the separation between the plates (d): C = e A / d for a parallel plate capacitor, where e is the permittivity of the insulating material (or DIELECTRIC) between the plates.Recall that we used Gauss's Law to calculate the magnitude of the electric field (E) between the plates of a charged capacitor: E = s / eo where the space between the plates is a vacuum.Vab = E d, so E = Vab /d