Introduction of Capacitance

Purpose:  We begin to investigate what capacitance is and how it is measured. We also go over some of the methods for finding the total capacitance of a number of capacitors, similar to how we found the equivalent resistance.

Quiz Problem

We begin by going over the quiz. The quiz tested our understand of using Kirchhoff's Laws. We had to create two loops in the circuit and write and equation depicting how the potential drops as we go through the loop. This drop should equal to zero. We, then, utilize the relationship between the currents and these three equations, we are able to find the values for the current at different positions. Once we have the current, we are able to measure potential and this allows us to measure how much power is generated by the circuit.

The Inside Of A Capacitor

Professor Mason takes apart a capacitor and we see that there are two conducting plates separated by some material called a dielectric. What the dielectric does is enhance the capacitance of the capacitor by altering the permittivity.  This is important because the capacitance is proportional to the permittivity. It is also proportional to the area of the plates and inversely proportional to the separation distance.

Finding The Capacitance

We decide to solve for the size of the plates needed in order to have a capacitance of one farad and a separation distance of 1 mm in a vacuum space. We found that we need a square sheet of length 3.55 miles. This seem outrageous. To compensate for the area of the sheet, we can put a dielectric between the sheets. This allows us to use a reasonable size sheet for the same amount of capacitance. This demonstrates the importance of dielectrics in capacitors.

Making A Homemade Capacitor

We begin a hands-on experiment by creating our own capacitors using two sheet of aluminum foil.

We use our lab manual to separate the aluminum. This means that the paper acts as a dielectric. The capacitance is then measured at several different separation distances.

The image shows how we placed the aluminum in the lab manual. WE made sure to stick in deep in the manual to prevent the two foils from touching. If they touch, no capacitance is created. We connect the foil to the multimeter to measure its capacitance.



We then created a chart that signified how the capacitance changes as the distance changes. This created an inverse graph that says, as the separation distance increases, the capacitance approaches zero. As the separation decreases, the capacitance approaches an infinite value. This proves the idea the capacitance is inversely proportional to the separation distance.



Our board shows some of the calculations we had to make in order to make the chart used in the previous picture.

Finding Equivalent Capacitance

Like we did with the resistors, we began to see how the total capacitance is found by orienting the capacitors in parallel and in series. We used the multimeter to find the total capacitance and found that the parallel orientation allows us to just add the capacitors to find the total capacitance. If that is the case, we see that this is opposite of the resistor, so we make a reasonable guess that the series orientation is found using inverse sum. This turns out to be true in the end.

We practice finding the equivalent capacitance of a random oriented layout of capacitance and, again, we must look at piece by piece until everything is simplified and we have one value for all of the capacitors.

An Exploding Capacitor

Professor Mason shows us what happens when we put too much potential in a capacitor. The capacitor ends up blowing up. The reason this occurs is because the space within the plates become conductive by a large electrical field. The electric field rips electrons apart causing the space to become conductive and this causes a short circuit, creating a spark.

Conclusion:  We found that Kirchhoff's Laws prove very useful when evaluating a circuit. We also found that the capacitance is proportional to the area and the permittivity and inversely proportional to the separation distance. The permittivity proves to be very useful because it allows us to make large capacitors without using miles of material. We, also, found the technique for find the equivalent capacitance. This is useful because we can configure capacitors in order to achieve the desired capacitance.