Circuits: Capacitors

These are the steps for Kirchhoff's Law. Because we do not know the direction of the current, for now, we guess. If our answer turns out negative, then the current goes in the opposite direction.

This is the Kirchhoff's Law in practice with an example problem. The law also states that I_1 = I_2 + I_3.

Another equation that is part of the law is Voltage - I_1*R_1 - I_2*R_2 = 0.

Next, Professor Mason introduced us to capacitors by showing us what is inside of one. There is a long film that stores all of the electrons and it is also wet to preserve the electrons. Once it goes dry, the capacitor no longer works efficiently. The solution that keeps the film wet is a dielectric.

These are the components of a capacitor.

These are the different types of capacitors displayed here. Each one has a different strength as well.

The green one is called a super capacitor and is the strongest capacitor available. Although small, it is quite heavy.

Below is an equation to evaluate the strength of a capacitor. C is the dielectric constant kappa times initial epsilon times the area all divided by a distance. The unit of measurement of capacitors are called Farads.

In this next activity, Professor Mason blows up the capacitor below to show the extent of its limit.

Below, we derived the electric field equation to find out how much charge is stored in a capacitor.

We have spoken about the constant for permitivity of free space but what are its units of measurement? Using the capacitor equation that we derived above, we were able to find them. Epsilon's unit of measurements are a Farad over a meter.

Next, we measured if capacitance depends on area or on separation by using a textbook, two sheets of aluminum foil, a multimeter, and a vernier caliper.

Utilizing the capacitor equation found before, we were able to determine the dielectric constant for paper. We also found that all of the units cancelled which made kappa a unit less variable.

The number displayed on the multimeter is the capacitance that was measured. We found that there was no possible way for it to stay constant long enough because of the pressure that was being applied by one of our group members.

We then continued to calculate the dielectric constant with different amounts of paper. But because it was difficult to find a constant capacitance value, it was difficult to determine whether the capacitance was indeed dependent on area or whether it was dependent on the separation.

Rearranging the capacitance equation, we were able to find the distance between the Gaussian surface and the capacitor with the given values. With that, we were then able to find the density.

We were also then able to find the charge inside the plates as well as the magnitude of the electric field using the kappa found earlier.

We were told that 20 horsepower was charged inside the plates of a capacitor for five hours. We were then asked to find the actual capacitance of the capacitor when the voltage was at 400.

With the equations shown below, we were asked what the relationship between kappa, capacitance and sigma was. We found that as kappa increases, then C will increase and thus, sigma will also increase. And what about voltage? Well, voltage, V, will decrease which results from: V = Q / C.