Chapter Eight electric fields and capacitance. Whenever an electric voltage exists between two separated conductors and electric field is present within the space between those conductors. In basically tronics, we study the interaction of voltage, current and resistance as they pertain to circuits, which are conductive paths to which electrons may travel. When we talk about fields, however, we're dealing with interactions that can spread across empty space. Admittedly, the concept of a field is somewhat abstract, at least with electric current, it's not too difficult to envision tiny particles called electrons, moving their way between the nuclei of atoms within a conductor, but a field doesn't have mass and may not exist within matter at all. capacitors are components designed to take advantage of this phenomenon.

By placing two conductive plates usually metal in Close proximity to each other. There may be different styles of capacitors construction, each one suited for particular ratings and purpose. for very small capacitors to circular plates and between insulating material will suffice. For larger capacitor values the plates may be strips of metal foil sandwich around flexible insulating medium and rolled up for compactness. The highest capacitance values are obtained by using microscopic thick thickness of layers of insulating oxide separating two conductive surfaces in any case, so, the general idea is the same two conductors separated by an insulator. So, simply put, capacitors are devices for storing electric charge.

Basically capacitors consists of two metal plates separated by an insulator they In the insulator is called a dielectric. And it's made up of, say polystyrene could be oil air, mica. There's several insulating materials out there that they use for the dielectric of a capacitor. There are a few things out there that affect a capacitor, one of them is the plate area, all other factors being equal, the greater the plate area gives greater capacitance and the less plate area gives less capacitance. Larger plate area results in more field flux, that is the charge collected on the plates for a given field force, which is the voltage across the plates. Now we're going to talk more about flux fields in a few slides.

But I just wanted to talk about the factors affecting capacitance right now. plate spacing, further plate spacing gives less capacitance and closer plate spacing gives greater capacitance. Closer spacing results in a greater field force, which is a factor of voltage across the capacitor divided by the distance between the plates. This results in a greater field flux, which is a function of the charge collected on the plates for any given voltage applied across the plates. And as I said, we'll talk more about field fluxes in a few more slides. dielectric material, all insulating material used in capacitor is rated as to its permittivity.

Permittivity is a measure of resistance that is encountered when forming electric field in a medium. In other words, permittivity is a measure of how electric field affects or is affected by dielectric medium. Greater permittivity of the dielectric gives greater capacitance less permittivity of the dielectric gives less capacitance. Although it's complicated to explain some materials offer less opposition to field flux for a given amount of force field. materials with greater permittivity allow for more field flux. Others offer less opposition and thus a greater collected charge.

For any given amount of field force applied voltage. relative permittivity means the permittivity of a material relative to that of a pure vacuum. The greater the number, the greater the permittivity of the material. Glass, for instance, with a relative permittivity of seven has seven times the permittivity of Israel. Vacuum while air has almost the same permittivity of a pure vacuum, and consequently will allow for the establishment of an electric field flux stronger than that of a vacuum, all other factors being equal. Here's a list of relative permittivity of various dielectrics from compared to a vacuum which relative permittivity is, air is 1.0006, which is almost the same as a vacuum.

Polyethylene is over two times what a vacuum is. wax paper is almost three times mica is 5.4 times glycerin is 43 and pure water is 80 and strontium titrate is 310 times and there are various assortments of capacitors out there that are constructed in many different ways and have maybe more than one leads coming and going to them and they are designed for special purposes and others are designed for quantity and in being able to use in various applications. Anyway, these are only a few of capacitors that are out there. And these are what they look like. When a voltage is applied across two plates of a capacitor, they concentrated field flux is created between them allowing a significant difference of free electrons a charge to develop between the two plates. As the electric field is established by the applied voltage, extra free electrons are forced to collect on the negative conductor while free electrons are running From the positive conductor, this differential charge equates to a storage of energy in the capacitor, representing the potential charge of electrons between the two plates.

The greater the difference of electrons on the opposing plates of the capacitor The greater the field flux. And the greater charge of energy, that will be stored by the capacitor. Because capacitors store the potential energy of accumulated electrons in the form of an electric field, they behave quite differently than resistors, which simply dissipate energy in the form of heat in a circuit. energy stored in a capacitor is a function of the voltage between the plates. A capacitors ability to store energy as a function of voltage, potential difference between the two leads results in a tendency to try to maintain the voltage at a constant level. In other words, capacitors tend to resist changes in voltage, whether it's drop or an increase, when voltage when the voltage across the capacitor is increased or decrease the capacity to resist the change by drawing current from the supply, supply and current in the source of a voltage charge in the opposite or in opposition to the charge.

To store more energy in a capacitor, the voltage across it must be increased. This means that more electrons must be added to the negative plate and more taken away from the positive plate necessitating a current in that direction. Conversely, to release energy from a capacitor, the voltage across it must be decreased. This means so The excess electrons on the negative plate must be returned to the positive place plate necessitating a current in the direct in that direction. Now, we would like to define capacitance, capacitance C of a capacitor is defined as the ratio of the magnitude of the charge on either conductor to the potential difference between the conductors. In other words, a capacitor is greater has greater capacitance, if more charge is accumulated using less voltage.

The SI unit of capacitance is a fair add and a fair add is a very large unit. So, common units out there are The micro farad which is equal to 10 to the minus six ferrets, the nano farad which is 10 to the minus nine fair ad and a pico farad which is equal to 10 to the minus 12 fair ads. Practically speaking however, capacitors will eventually lose their storage voltage charges due to internal leakage paths for electrons to flow from one plate to the other. Depending on the specific type of capacitor the time taken for stored voltage charge to dissipate can be a long time even several years with capacitors sitting on a shelf. When the voltage across the capacitor is increased, it draws current from the rest of the circuit acting as a power load. In this condition, that capacitor is said to be charging because there is an increased amount of energy being stored in its electric field.

Conversely, when the voltage across the capacitor is decreased, the capacitor supplies current to the rest of the circuit, acting as a power source. In this condition that capacitor is said to be discharging, it stored energy held in the electric field is decreasing now as energy is released into the rest of the circuit, if a source of voltage is suddenly applied to an uncharged capacitor, a sudden increase in voltage, the capacitor will draw current from that source absorbing energy from it until the capacitors voltage equals out of the source. Once the capacitors voltage reaches this final charge state, its current decays to zero. Conversely, if a load resistance is connected to a charge capacitor, the source of voltage is suddenly removed, that capacitor will supply current to that load until it has released. All its stored energy and its voltage decays to zero. Once a capacitor voltage reaches this final discharge state, the current decays to zero in their ability to be charged and discharged capacitors can be thought of as acting somewhat like secondary cell batteries.

The choice of insulating material between the plates, as was mentioned before has a great impact upon how much field flux and never how much charge will develop with any given amount of voltage applied across the plates. Of course, when this charging takes place, there's always some reason assistance in the charging circuit even if it's only the resistance of the wire connecting the supply voltage to the capacitor as you can see in the little diagram that I have up at the top there, the supply voltage of courses the battery and the resistance whether it's a bulk piece of resistance or the wire is shown in the diagram in series with the capacitor. That resistance will determine the speed at which a capacitor charges along with the size of the capacitor Of course, the mathematical formula for this charging curve and its plot of charging voltage versus time is showing here.

V is the capacitor or the voltage across the capacitor. vs is the supply voltage or the battery in this case, and r is the resistance of the circuit see is the capacitance and he is a well known mathematical constant that fell over the development of this, this formula, and it's just a number and the number is approximately 2.718281828. And it goes on forever. But that's a good enough approximation. You can see that at time equals zero, e to the minus zero is one, therefore v is zero. at infinity after a long period of time of this charging, e to the infinity is zero.

So the voltage across the capacitor course just equals the supply voltage, which is kind of intuitive. Anyway, we knew that at the beginning. Also, because the charge on the plates is directly proportional to the voltage across the plates. Then this curve also describes this charging Or the rate of charge of the that or that is on the plates. Of course it has to be scaled. But it the curve is it's the same curve in calculating the charge on the plates.

Now the current flowing to the capacitor will fall off over time and eventually it'll go to zero as the capacitor is fully fully charged. But this curve describes the current to the capacitor. And you can see at at time zero, the term is is equal to I naught which is the current at the beginning of the when that switches first close to the, to the discharge capacitor and it starts to charge. The current will be fully at time zero, fully dependent on only the resistor and voltage of the battery, which we could just use ohms law to describe which is the supply voltage over the resistance of the circuit. But immediately once it starts to charge of course the current starts to fall off and as it approaches infinity or after a long period of time, the current will be zero as I said and the that will happen when the capacitor is fully charged and the voltage across the capacitor is equal to the voltage of the supply.

Let's see what happens when we connect ups capacitors in series as we see here we have C one c two c three in series with a DC supply voltage. As the voltage is applied to this series circuit, charges will tend to flow and migrate and what happens here is the charges will be equal. In other words, looking at C one, the positive charge on C one plate is going to be equal to the positive charge on C two is equal to the positive charge on C three is also equal and opposite in charge to the opposite plates. If they were not equal, they would tend to push charges until they were equal. So logically speaking, all of the plates have to have an equal amount of charges on it. So if we were to define a term of a capacitor having charges, then the total charge across the total three capacitors is given by the positive plus charges on the C one plate and the negative q on the C three plates so that we might say that q t is going to be equal to q1, q2 and q3.

If that was not the case, then they would, you'd have a buildup of charge in a wire and it just can't happen. So, we can say that Qt is equal to q1 is equal to q two is equal to q three which is the charging of the plates. Now, according to current shops Voltage Law around the loop, the voltage drops v one v two v three have to equal the supply voltage. So, you have the total voltage supply voltage is equal to v one plus v two plus three. Remember that a capacitor is defined as the charge over the voltage of the capacitor, we can rewrite that equation now, so, we can say the voltage across each capacitor is going to be or the total capacitance even is q See. So we can now rewrite our voltage equation that we have from cross Voltage Law in terms of the charges and the capacitors.

So what we have is a total charge q t all over C, which is the total capacitance of the series circuit is equal to the sum of the individual charges over the individual capacitors, or Qt over c is equal to q one over c one plus q two over c two plus q three all over c three. Now, we know that q t for the total is the same as the individual charges on each individual capacitors we've already gone through that logic. So we can replace q1 q2 q3 with their equivalent Qt. So the equation now becomes Qt all over c is equal to Qt over c one plus Qt Qt over c two plus Qt all over c three. And if we divide both sides of the equations by Qt, the equation still holds true, which says one over c is equal to that which is a total capacitance is given by one over c one plus one over c two plus one over c three.

So, you can now calculate what the the result of connecting three capacitors up in series is given by this equation that you see in front of you, which is not too unlike what we get with resistors when we could connect them up in parallel. But, in this case, we're connecting this capacitors up in series and this is how you calculate the total capacitance of the three capacitors. Okay, let's see what happens when we connect capacitors up in parallel, as we see here in the diagram c one c two c three are connected in parallel across a DC supply voltage which has a voltage V. We know that the definition of capacitance is given by q, the charge of the capacitor the charge in the capacitor over the voltage drop across that capacitor. In our diagram here, we if we designate the sum of the capacitance of the three capacitors as C subscript t, then it's going to be equal to the total charge over the voltage and the voltage across each capacitor is the same and that's equal to the supply voltage We know that the total charge is going to be made up of the charge of capacitor one, capacitor two capacitor three, so we have q one plus q two plus q three, all over V would be the capacitance of the three capacitors in parallel.

We can rewrite that equation and break out to three individual quantities where q1 is now over v plus q2 over v plus q3 over V, which is the same equation that is above. Except in this case, you can see that q one over V is the capacitance of C one, q two over V is the capacitance of C two, and Q three over V is the capacitance of C three. So we can then rewrite the equation such that the total capacitance is given by C one plus c two plus c three which is similar to a series circuit of resistors, where you would add up the resistors to calculate the the total resistance in that circuit. In the case of a parallel connection of capacitors, you add the capacitors up. Before finishing off the chapter, I thought we just have a quick look at some of the different uses of capacitors that are out there in the tuning of radio stations, and there's still some being used are still some using this method today.

Although it was more prevalent in days gone by, in a in a tube radio with they used to call a superheterodyne. Radio they had meshing of plates that varied the capacitance of the the tuner and these plates would actually move in close to each other and And away from each other. So you'd vary the distance between the plates, as well as the area of the plates as you turn the knob. And that would actually vary the capacitance which was in the tune circuit, and you could tune in the various radio stations that way. Another use even today is in the keyboard. Some keyboards have each key is connected to a plate, a small little plate and as you press the key down, you vary the the capacitance of that individual button.

And there's a receiver that converts that capacitance into a signal that recognizes as that particular key that you've pressed and converts it into what is required by the computer. Another application that has been used out there is the condenser microphone, and the plate of a microphone pickup would vary as the sound waves would hit it and as varying the distance between to place you would vary the capacitance and that would be detected as a signal which could be amplified and used for various electronic devices such as a recording or talking over distances etc etc. Another application is the electronic flash for cameras. These are nothing more than a great big capacitor that once it's charged, it will then have work as a large power supply and it would actually when the shutter is pressed, the there would be a big dump of the of the power or the electric electric charge on the capacitor into the light tube and that would flash and give you the the required lighting for A flash circuit.

So, this ends chapter eight