Capacitors and Capcitance

The day began with a recap on capacitors and capacitance. We began by doing some work on the lab manual predicting how capacitors would behave and constructing a graph representing how the brightness of a bulb would change over time if a charged capacitor was input into a closed circuit as a power source. We predicted that the brightness would decrease at an exponential rate until the capacitor ran out of power. We also found that the voltage would remain the same throughout the close circuit and as a result the charge would also remain the same, which goes back to the basics of current and voltage learned at the beginning. We also recapped on the behavior of capacitors in series and in parallel. We said that when capacitors were in series, the voltage increases because as the capacitance decreases, the charge remains the same and the voltage gets larger and it would work the opposite for capacitors in parallel. Finally, we measured some of the voltage of batteries in order to see whether our predictions made sense since capacitors also work as batteries.

Below is a picture of the set up we had in order to test for the voltage of the closed circuit.

In order to further understand the behavior of capacitors, Mason decided to let us use Logger Pro and graph the behavior of the capacitors as time increases when a capacitor was charging and when it was losing power. The graph below shows the graph of when the capacitor was decreasing in electric potential, or discharging. 

Below is a data table of the points that were used to make the graph above.

Below is a picture of how the set up was made when we were measuring for the electric potential of the capacitor when charging or when discharging.

The graph of the capacitor charging is shown below. As time increases, the electric potential grows exponentially meaning that potential energy is being stored within the capacitor until it reaches the maximum charge it can hold.

The data table of the data points for the graph above are shown below.

After looking at the behavior of the graphs, we can finally use Logger Pro and construct the best fit for the graphs and thus it led to the theory of exponential decay which showed how the voltage decreases over a period of time. All the derivations are shown below.

Then we decided to work with the theory of exponential decay and solve a problem which asked to find many unknown variables within that equation. We also graphed the relationship between voltage, brightness and current with respect to time with respect to the exponential decay.

Overall, we learned more about capacitors but the main focus of the class was showing how capacitors gained or lost charge and relating it to exponential decay and charge buildup

Kirchhoff's Rules and Capacitors

The day began with a quiz about Kirchhoff's rules and we solved the problem as a class. We began by finding the the current between the two loops in the parallel circuit. We then found that the negative current of the bottom lop plus the current of the top loop is equal to the total current around the whole circuit. Using those equations we were able to solve for the voltage through the top and bottom lop as well as the power of the top and bottom loop. The results are shown below.

We then moved on the topic of capacitors. Capacitors are devices that store electrical charge and electrical potential energy. Mason gave us a relationship between voltage, charge and capacitance which was Q=CV. We were also derive that further by using the definition for charge and voltage into the equation C=kEA/d. We also did our own experiment were we created our own capacitor using two sheets of tin foil in between pages of the lab manual. We recorded the capacitance in nF and drew a graph that compared the relationship between distance and capacitance and drew our conclusions that as distance increases, capacitance decreases.

Next we solved our problem using our new definition for capacitance in order to find the area of a given object. Then we began to learn about relationships between capacitance and circuits and how they behave in parallel and in series.

The capacitors behaved oppositely to the way resistors behaved. When capacitors are in series, the inverse of the total capacitance is equal to the total sum of the inverse of all the capacitors and when capacitors are in parallel, the total capacitance is equal to the sum of all the capacitors. Then, we solved a problem very similar to a resistor one we had.

Finally, we applied Kirchhoff's Rule to a closed circuit with capacitors. Using previous methods, we solved for the voltage across the whole circuit as well as the total energy.

Overall, we learned about capacitors and how to use them within a closed circuit and then we applied Kirchhoff's Rules to a closed circuit involving capacitors instead of resistors.

DC Circuits, Resistors and Kirchhoff's Rules

The day began by talking more about closed circuits and Mason gave the class two set-ups of two circuits each with an on and off switch and these paths were a little more complex than the usual ones he gave us. We were supposed to predict which one of the light bulbs was going to be dimmer and which one was going to be brighter. For the first one we predicted that the light bulb in the top was going to be dimmer because it had a longer path to flow through while the upper light bulb was going to be brighter since it had a smaller path. We also had to predict what would happen to the middle light bulb if the switch was off. We said that the flow of energy was not going in a complete circuit if the switch was off and therefore the light bulb was not going to turn on. For the second set up we had a more complex set-up and we were again supposed to predict which one of the light bulbs was going to be dimmer and which one was going to be brighter if the switch was flipped from off to on. We agreed that the upper light bulb had to be brighter because another flow of electricity was going through that bulb and the lower bulb would have the same amount of light because the path would remain the same.

Using our previous knowledge we then made a chart on how the light bulbs were going to act if they were set up in parallel or series and we agreed that putting light bulbs in series result in the light bulbs being dim, where setting them up in parallel results in the opposite whereas setting the batteries in parallel results in dimmer batteries where setting the batteries up in parallel does the opposite. We also moved on to the topic of resistors and we talked about how to calculate the resistance by looking at the color scheme of each of the capacitors. Our results are shown in the table below.

We then used a multimeter in order to get the exact resistance of each of the resistors using a DC circuit. The multimeter is shown below.

The results from each of our finding is in the upper right hand corner of the picture and it shows that resistors in parallel decreases in value whereas resistors in series increase in value. The relationship as a result is total resistance in a series is the sum of all the resistors while the inverse of total resistance is the sum of all the inverses of the resistors.

The relationship explained previously is put into effect into the problem below. It shows a variety of resistors and we were supposed to solve the total resistance found in the whole system. By using these rules, we came to a value of 100 Ohms.

The day ended by talking about Kirchhoff's Rules which talked about how to find the current, voltage and work of the system. The whole process of how to use these rules involved tracing one flow of current through one loop and tracing another flow of current through another loop. Then using the other rules from before knowing that the current is the same in a series and that the sum of the current in each of the loops is the same as the total current in the whole system one can combine all the equations to solve for multiple unknowns.

Overall, we learned about current through a DC circuit as well as resistors and how resistors in a series and parallel add up. Finally, and probably the most important part of the class, involved Kirchhoff's Rules and how they are used to solve for multiple things in a closed circuit.

Potential and Continuous Charge Distribution

After talking about charges and electric fields on point particles, we moved on to continuous charge distributions. We began with a uniform ring and a point particle a distance x away. The radius of the ring was a and the ring had a charge of q. Since the distance x from the particle and the radius of the ring make a right triangle, the hypotenuse of the triangle would be the distance between the point particle and the charged ring. In order to find the potential, the charge needs to be known and by plugging it in we can get a result. We also moved the point particle up and added an angle between and solved for the charge as well.

Then we used the previous relationships for solving the potential in order to get to the same result. Using the equation of the integral of the energy field multiplied by the change in distance we came to the same equation of some constant K times the charge over the distance is equal to the potential as well.

Next we moved on to a uniform bar and a point particle an x and y distance away from it. The distance change of course sine the bar is uniform and the distance, unlike a circle, does not remain constant. In this case, we had to replace the change in q with some constant lambda dimes the change in the x direction (y is not needed since that distance does not remain the same). We solved for the x value using Wolfram Alpha and found the potential using the known values. We also went ahead and drew some electric field directions between two equipotential particles.

The day ended after we used a volt meter in order to map out the voltage in respect to the electric fields made by the two "point particles." The set-up is shown below. We were supposed to map the distance and voltage into a table.

The result table is shown below. It is shown that as the distance increases so does the voltage.

The main focus of the class period was to know how charge affects continuous objects and finding problem solving techniques so that we can solve said problems. We also had a visual understanding of electric fields as well as finding electric potential values between each of the charges.

Electric Fields and Force

We began class with another closed circuit set-up but the goal was to set it up so that both light bulbs used were as bright as possible and as dim as possible. One of the set-ups is shown below and it involves that of a parallel set-up.

We then drew both of the set-ups as well as the circuit diagrams that coincided with them and labeled them as dim and bright. The parallel set-up proved to have dim light bulbs while the direct set up proved to have the brightest light bulbs.

 

We moved on to predict what a change in temperature between water within a styrofoam cup and electricity needed to have in order to solve for it. Our group predicted that a mass, time and power were needed in order to solve for it. We also recapped on Ohm's Law and showed how a current could be found by knowing the voltage and resistance. We also recapped about the equation P=IV and how when the voltage is increased, the current is also increased (which is common sense).

The main focus of the class though was regarding the relationship between work, energy, force and electric fields. The work is also defined as the integral of force dot the change in distance or force times distance times the cosine of the angle between the two vectors. This can be also translated into en electrical perspective which is the integral of an initial charge time the energy field value times a a change in distance. We reviewed force by working on a problem that dealt with F=ma. We also talked about electric potential energy and how it equals to negative work which also equals to the previous relationships discussed and as a result the final product would be one charge times a constant K times another charge over the distance between the two particles. We also talked about the how voltage is equal to electric potential over the charge of one particles which is also equal to a constant K times the charge of the particles over the distance.

We then decided to prove that the integral of the energy field times the change in distance is equal to some constant K times a charge over the distance. The result is shown below.

We then decided to take Python and plug in some charges as well as other bigger charges a certain distance away from the initial charges and find the electric potential of each respectively. The results are shown below.

Mason also asked us to predict what the picture would look like before we used Python to get the results. We also showed the manual calculation for one of the electric potential values.

Overall, the main focus of the class period was regarding electric fields and the relationship between work, force and electric potential energy. We also reviewed some of the power functions as well as Ohm's law.

Current, Voltage and Resistance

The class began with a video about new college graduates and how most of the engineering majors could not light a light bulb with just a battery, a wire and of course a light bulb. The reason behind why most graduates could not accomplish such a feat is because they have not received the proper education or they just never got anything out of their classes. Mason decided to let the class try so that we are not caught off guard like those students were. Unlike them, we were successful as shown in the picture below.

The reason why the students did not succeed was because most did not have a closed circuit. A closed circuit is crucial because otherwise the electrons would not flow from one terminal to the other since the ends are not together. In order for the light bulb to light, the circuit needs to be closed which allows the flow of electrons to connect with the least amount of resistance because air has a high resistance value meaning that the electrons would not be able to connect.

Then Mason asked the class to show two set-ups where lighting up a light bulb would light up and two more where the light bulb would not. We then explained why was it that the light bulbs did not light and we answered that it was because the electricity did not flow through the filaments.

 Then we moved on to the current of a closed circuit. We were able to measure the value of the current by using an ammeter and the same set-up as before for the closed circuit. The current was measured in Amps. A picture of the set-up is shown below.

We continued with the topic of current and added voltage and power to the equation which all falls into the equation of P=IV or power is equal to current times voltage. The picture below shows the different units used for each of the variables. We also solved an easier problem involving finding the power using a known voltage value and a known current.

Finally, we ended the day by talking about drift velocity as well as the relationship between voltage and current. We found that the current is the same as the change of current over the change in time. Again we solve an easy problem involving finding the drift velocity through a wire. By knowing what kind of wire it was and having known values we plugged them in into the equation and solved for the drift velocity. We also found that the voltage is equal to the current times a constant, which is resistance measured in Ohms and is also referred to Ohm's Law or V=IR

Overall, the main focus of the class was to introduce us to electricity by learning about closed circuits, voltage, current, power and learning about Ohm's law and resistance.

Electric Charge and Force

The class began by continuing on more information regarding electric fields and dealing with uniform objects.

First, we predicted what an electron would do if passing through two bars of negative and positive charge. We also found an equation regarding a particle moving through many directional charges. Our work is shown above.

We then had another programming activity regarding two spheres and an electric field around them pointing around in a circle. The predictions of how it would look like are shown in the picture above. 

The picture above shows an exercise that Professor Mason gave us to do regarding the faces of every solid given to us. This probably was to introduce us to charges on the faces of solids.