Today we learned about capacitors. These are a couple of conductors that are charged up one with positive charges and the other with negative chargers. These are close enough to each other so that they have an electric field between them. For convenience, we'll deal with those that are parallel to each other. These could be flat plates, cylindrical surfaces, or amorphous surfaces that are next to each other. Examples of these are in the picture below.
Prof. Mason opened up a real life capacitor for us. It looked like a couple of long metal plates that were sandwiching a fiber in between which didn't let them touch each other. Also, it was wet. The reason is that it is a dielectric capacitor and it had dielectric fluid. These were very long and the purpose of this is to increase surface area and reduce the volume so as to have as much capacitance in a small volume and with little weight.
These capacitors are the ones that look blue in the pictures. The green capacitor is called a superconductor because it has a lot more capacitance than the others in a very tight space.
So, we studied the theory behind these electrical behaviors. When we have a couple of charged conductors, one with positive charge and one with negative charge, an electric field is present. If these conductors are parallel plates, then we can easily compute a lot things like the difference in voltage.
We didn't know before, but these can actually explode. Prof. Mason put a protective screen and got everyone behind him so as to avoid any possible injuries and ensure the safety of his students. This is the thick plastic seen in the picture below.
The capacitor is the small black cylinder with a couple of metals coming out, one was connected to the positive side of the battery and the other was connected to the negative side of the battery.
When Prof. Mason reversed the polarity on the capacitor, it took a few minutes for the capacitor to make a cracking sound and explode. Below there are a couple of pictures of what it looked like after it exploded.
Then we developed formulas that will help us calculate lots of useful stuff that deals with capacitance. We calculated using calculus the relationship between the electric field, the charge and the capacitance. Then, we did some algebra to find more useful relationships.
Then we studied a little bit about capacitors themselves. Since they have charges and electric fields, capacitance must be related to the surface area of the plates. A larger surface area will yield a larger electric field and allow more charges within it. Also, when the distance between the plates increases, the electric field between them decreases. If we define the capacitance as proportional to these variables, then we the relationship denoted below. However, there is a constant of proportionality called the permitivity space. Also, this value is dependent on k, the dielectric constant, and the permitivity of free space.
Then, we did an experiment where we calculated the dielectric constant of paper. For this, we cut a couple of metal plates which were aluminum foil paper. We made them the size of paper and putted several sheets of paper between them. These would create a capacitor. Then we connected an electric source and measured the capacitance with a voltmeter. We also measured the thickness of paper since this is the distance between our metal plates. We did this while having 1, 2, 3, and 4 pages in between to obtain several data points. Then, the value of kappa was calculated for each one.
Then we did another exercise with capacitance. In here we calculated the distance between the plates, the charge density, magnitude of the electric field, and energy stored.
Then we did another exercise with capacitance where we wanted to calculate the capacitance of a car battery that would run based only on the storage of the capacitor.
Then we did another exercise where we calculated the effect of having a dielectric in between the metal plates. In there we saw the effect of the dielectric on the capacitance, voltage, and charge density.
Summary
Today we saw lots of cool things and learned new things. We learned what a capacitor is and how it works. And, we saw how it looks like inside. Then we developed the relationships capacitance has with voltage, electric field, energy, and physical constants. Finally we worked with a few problems to get us familiarized with the concepts and behavior of particles when there is a capacitor present.
