5.2 Capacitance from Office of Academic Technologies on Vimeo.
5.02 Capacitance
All right. Now, let’s continue with the concept of capacitance. Let’s consider two conducting plates, two conducting parallel plates, and I will draw these plates such that their thickness is exaggerated. Let’s say this is one of our plates, the upper plate, and this is our lower plate. Let’s draw this one’s thickness also in an exaggerated way.
Let’s assume that we connect these plates to the terminals of a power supply, like a battery. Let’s assume that we connect the upper one to the positive terminal of a power supply of a battery and, similarly, the lower one to the negative terminal of the same battery. Whenever we do this, since we have a positive charge concentration at the positive terminal of the battery, these charges are continuously repelling one another. And whenever they see a path they can move, this conducting path, a piece of wire, therefore they flow or move through this path and then they start to get collected throughout these conducting plates.
Since they also continuously repel one another, then they’d like to go as far away as possible from each other and therefore they end up by getting collected and then uniformly distributed along the lower surface of this upper plate. Similarly, the negative charges are repelling one another through this negative terminal. And whenever we connect and provide a path for them to move, therefore they move along this conducting path, they get to be collected in this case along the upper surface of this lower plate. They distribute themselves uniformly, again, and this is the maximum distance that they can go away from each other. Therefore as a result of this, the upper surface of this lower plate gets charged negatively up to some certain q value.
Now, of course, this charging process continues until the plates reach to a high enough charge density so that they can generate high enough repulsive force to the incoming charges. And at that instant, then the charging process stops and these plates therefore get, or reach, their maximum charge. If we call the amount of charge to be collected on these plates as q, of course the upper one will get charged to a positive while the lower one is going to get charged to negative q value, since these are the terminals of the same power supply.
Once the plates start to get charged, naturally we are going to generate an electric field associated with these charges, which will be pointing from positive plate and towards a negative plate, filling the region between these two conducting plates. Therefore this volume between these two charged plates will get filled up with the electric field pointing from positive plate towards the negative plate.
Since we know that the potential associated with the positive charge is greater than the negative charge, because if we recall that for the point charges, the potential of the point charge was q over 4 Pi Epsilon zero r, whereas the potential of a negative charge was minus q over 4 Pi Epsilon zero r. So we’re going to end up with a potential difference between these two plates, since the positively charged plate will have greater potential than the negatively charged plate. This process, therefore, will generate a potential difference. Let’s call that difference as V between these two charged plates.
Of course, when the plates were neutral, when they were not charged, then they were both at the same zero potential and the potential difference between the plates was just zero. Therefore let’s just go ahead and say that V represents over here as the potential difference between the plates, and the E is, of course, the electric field.
It is also easier to see that the more charge that we end up stored on these plates will result with a greater potential difference generated between the plates. We can say that the charge will generate a potential difference, and the amount or magnitude of charge that we store in these plates is directly proportional to the potential difference generated between the plates.
Well, if we do this experiment over and over and over again, then we can find proportionality constant in order to represent this proportionality in the form of an equation such that q is equal to C times CV. Here, C is the proportionality constant. Now if we solve for C, that’s going to be equal to the amount of charge stored on the plate of this system divided by the potential difference between the plates. We have a special name for the proportionality constant; it is called capacitance.
If we look at the units of capacitance in SI unit system, since the unit of charge is in Coulombs in SI unit system, and the unit of potential is in volts, therefore Coulomb per volt is what we call the unit of capacitance. We have a special name for this ratio. It is called farad. Therefore 1 Coulomb per 1 volt is what we define as 1 farad.
Now these are very large quantities. In other words, 1 Coulomb is a huge amount of charge and 1 volt is basically a small potential difference. Therefore this ratio, which is corresponding to 1 farad, is a very high capacitance value. In general, we deal with the capacitances associated with capacitors on the order of microfarad, which is 10 to the minus 6 farad, or picofarad, the typical values associated with the capacitors, which is 10 to the minus 12 farad.
So a system like this, two parallel conducting plates separated by a small insulating medium–in this case it is air–represents what we call a capacitor. The capacitance of a specific capacitor is determined from the geometry of the plates, and we will see how to determine this quantity relative to the different types of capacitors.