RC Circuits

     This is the setup for the lab we conducted on Monday in which we were to create graphs of  a capacitor's charging and discharging times using LoggerPro.

 

     This is the graph of electric potential vs. time that was created during the experiment. It shows that a capacitor charges and discharges not linearly, but asymptotically. It also shows that the charging and discharging levels off at a certain point and that the capacitor will never really reach its maximum charge.

      After the experiment was completed, we compared the value of "c" from the fit equation of the discharging graph to a value we calculated from the values of the components used in the experiment. Because the numbers are so small, there is actually quite a large percentage error of about 32% if our calculated value of .01027 is taken to be the "true" value.

Capacitance

 

     On Monday, we conducted an experiment in which we turned a book into a capacitor. It is difficult to see from the picture, but there are two sheets of aluminum foil of equal area inserted into the book with pages in between them. 

 

     This is a chart of the capacitance we measured using our capacitor. For the first part, we increased the distance between the plates with the initial distance being the thickness of 10 pages. For the second part, we halved the area of the plates by simply folding the foil in half. We also attempted to calculate the true value of "k" for aluminum foil using some of our data. We were off by about a factor of three.  

 

     The above picture is a graph of capacitance vs. distance. The graph shows that capacitance is inversely proportional to the distance between the plates just as we expected it to be. 

DC Circuits

      On Wednesday, we were given a series-parallel circuit and were asked to compute the equivalent resistance of the entire circuit. We broke it down into parts in order to make that computation, and those calculations can be seen in the picture above. Then, we made the circuit by twisting resistors together, measured the total resistance, and compared it to our calculated value. Those values can be seen in the lower right hand corner of the whiteboard.

 

      The two pictures above are pictures of an exercise we also completed on Wednesday. We constructed the circuits from the schematics seen in the picture and analyzed voltage and current in both series and parallel circuits. We found that the sum of the potentials across the resistors in a series circuit equals the input voltage, and that the current is the same in all components in a series circuit. We found that the opposite was true for parallel circuits. Specifically, the sum of the currents in a parallel circuit equals the input current, and the potential is the same across all resistors in a parallel circuit.

 

     We were given another circuit and were asked to compute the three unknown currents using Kirchhoff's laws. We were then to build the circuit on a breadboard, and actually measure the currents and compare them to our measured values. However, this is still a work in progress, and a picture of the circuit can be seen below. 

 

     Our calculated values for the currents I_1, I_2, and I_3 were 1.14 amps, .999 amps, and .138 amps respectively. Upon actually breaking the circuit at the necessary points in order to measure these currents, I found that I_1, I_2, and I_3, were 1.12 amps, .99 amps, and .11 amps respectively.  

Electric potential

     The above picture shows the data collected and the graph constructed from that data for the experiment we performed on Monday. The setup of the experiment involved a DC power supply which was set to 15 volts, a multimeter, and a sheet of conductive paper pinned to a piece of particle board. The positive end of the power supply was connected to a silver painted line on the paper, and the negative end was connected to a circular painted point on the paper. We began testing the potential at the circular point and moved the positive lead of the multimeter away from the circular point in 1cm increments until we reached the silver painted line. We recorded the potential for each of these distances in excel and constructed a graph of Potential vs. Distance, which can be seen in the picture.

More Power

     We had a lovely fiesta this past Wednesday! Instead of taking a typical quiz, we were given the materials shown in the above picture and asked to construct a circuit which lit the light bulbs as dimly as possible. In order to do this, we simply connected the two batteries in parallel and hooked them up to the two light bulbs which were connected in series. 

 

     There was also an experiment performed on Wednesday which involved a resistive coil that would heat a known mass of water when voltage was applied to it. We were given the mass of the water, the dimensions of the coil, and the applied voltage. Our goal was to determine the change in temperature of the water with our given information after a period of ten minutes had elapsed. We first determined the resistance of the coil and the current flowing through it. Because other groups had used a different value of resistivity and calculated a different current, we used these two values to come up with an uncertainty for the current. We then determined the power, the energy put into the water, and finally the change in temperature with uncertainty. The actual change in temperature was 2.5 degrees Celsius, but we calculated a change of 2 + or - .49 degrees Celsius. We went through the same process with an initial voltage of 9 volts instead of 4.5 volts. Those calculations are seen in the upper portion of the whiteboard. Doubling the voltage did not double the change in temperature. My intuition told me it would not because doubling the voltage, doubles the current, which increases the power by a factor of four.

      These are some hotdogs with 120 volts passing through them. The longer, thinner one cooked more quickly because it had more resistance than the shorter one with a greater cross sectional area. Some LEDs were placed into the hot dog to show that the further the leads of the LED were placed from each other, the greater the electric potential would be between the two leads. This was proven by observing that the LED with its leads positioned furthest apart burned out almost immediately.

 

Power and Ohm's Law

     This is a picture of the data we collected during our first experiment on Monday and the graph we created using that data. The circuit consisted of a power supply in series with a home made resistor and an ammeter. We measured the voltage across the resistor with various input voltages. We then calculated the power by using this voltage and the measured current and made a graph of voltage vs. current. This graph shows the voltage and current are directly proportional, and also that power is directly proportional to their product. The second set of data points came from the group across from us.

     We also performed a lab on Monday in which we measured the resistance of several different coils of wire with varying cross sections, lengths, and material properties. The above picture shows a graph of resistance vs. length. This was the graph that came out the best and shows that resistance is indeed directly proportional to length just as we suspected.

Last Lecture Before the Celebration

     In addition to microwaving a number of things in class last Wednesday, we also answered some questions from ActivPhysics as a group. The questions concerned the electric fields inside and outside of both an insulating sphere and a conducting sphere. The answers to these questions are pictured above.