6/2 LRC Circuit

Using our kinematics formula for frequency, we found a relationship between impedance and current. We then used the derived relationship to find what our current would be if the frequency doubled. We found that the current doubled as well.

We measured the current and voltage of a circuit consisting of a resistor, frequency generator, and capacitor. The frequency generator was set at 10 Hz.

The above two graphs were measuring current and potential vs. time measured from 1000 Hz. 

We created a table with all the values at different frequencies. We calculated theoretical values and experimental values for both 10 Hz and 1 kHz. Our theoretical impedance compared to our experimental impedance ended up having a 834% error. We deduced that this large % error is due to the unknown resistance in the frequency generator. We then calculated the phase change on the bottom of our voltage and current graphs.

When our capacitive reactance and inductive reactance are the same, we have graphs that theoretically should line up perfectly.

We solved for the power dissipated in the circuit but since our resistor is the only part of the circuit dissipating power, we cannot use the formula V = IP. We had to use a new formula P = IR.

We repeated the experiment with an inductor included in the circuit. 

5/28 Alternating Current (AC)

We solved for the formula to calculate the root-mean-square value for current and voltage.

We setup an experiment to calculate the RMS values for current and voltage using the function generator to produce a constant voltage and a closed circuit provided. We used a voltage meter and used logger pro to find our rms value for the voltage.

We took values from our graphs in logger pro to calculate the RMS for voltage and current. We know our max voltage is slightly less than the one indicated on the function generator and took that into consideration when calculating for our RMS of voltage. We found that our experimental value for the RMS of voltage is exactly the same as our theoretical value. We then found the current and noticed that there was a small difference between our theoretical and experimental values. We then drew the graphs of voltage, current, and voltage and current superimposed vs time. We found that the voltage and current, when superimposed make the positive x-axis.

We used the RMS of voltage and current and derived an equation to solve for the capacitor reactance. We then used what we derived here to solve a problem with the given values on the top right corner. We then used this derived formula on our next experiment.

We repeated the same experiment but included a capacitor. We found 3 RMS values for current, 1 from the graph in logger pro, another from calculations, and another from reading the voltmeter. We found that all 3 values varied slightly from each other but are within margin of error. We then found the phase change between the graphs we had of potential and current. Note: The phase change we calculated for in this experiment is incorrect. Instead of adding we should have subtracted.

From our previous experiments, we found that electric potential is a sine graph and current is a cosine graph. From this, we determined that current must be a function relating to cosine and electric potential must relate to sine and we derived their respective equations on the left. On the right, we took given values from a problem in class that would use our derived formulas to find the RMS of current.

We repeated our experiment once more, this time comparing the RMS values of electric potential. For our theoretical values, we found that our inductance value was off because the original percent error was too great. Instead of calculating for the RMS of electric potential, we instead found the correct inductance value. Because we used the value from the graph, our experimental value and theoretical value for voltage are the same hence the 0% error. The formulas we used and the givens are written in dark blue on the left. We also calculated for phase change on the bottom right.

5/26 Resistor and Inductor Circuits (RL Circuits)

We found that the color combination for a 100 ohm resistor was brown black brown. In red, we found the resistivity of an 18 gauge copper resistor by using the formula R = rho * L / Area and finding each variable to find R. We then calculated for the time constant, Tau. We were then given an inductor with a given inductance and asked to find the time constant. We found that the total resistance is 100 ohms plus 50 ohms from the resistance inside the oscilloscope.

We were given an inductor with 440 turns. We measured its length, area inductance and resistivity and plugged it into the  provided formula to find our theoretical results in red. We then used the oscilloscope to find our experimental values. We found that the calculated number of turns was about 70 turns off from our given 440 turns. Because of this inaccuracy, we had uncertainties in our inductance value and halftime.

In purple on the top left, we put in our own words what we thought Faraday's Law of Induction was. We were then given a circuit consisting of a battery, 2 resistors and 1 inductor. We calculated our max current for I2 and I3. Since the max of I1 is the sum of I2 and I3, we did not put that on the board. We then found current at 170 milliseconds. We used the time constant we calculated for in light blue on the top right to find current at a certain time. We then calculated for what the voltage would be if the voltage before the inductor is 11 volts. We found that the voltage in the inductor is 34 volts.

5/19 Electromagnet Induction

We answered 13 questions from the website on Robert's laptop. The interactive graph on the website showed us the relationship between emf and flux.

We did another series of questions on the same website. This time it was to find how inductors and resistors affected the current through a closed circuit. We found that the area of the inductor directly relates to the magnetic flux. If area increases, the flux increases and vice versa. 

We sent a current counterclockwise around the magnet and saw that it created an electromagnetic force pulling the rod toward the magnet.

We then reversed the current's direction and found that it produced an emf pushing the rod away from the magnet.

On the left, we found the relationship between an induced current and an induced voltage. In light green, we found the inductance, L, of the rod when given the length, radius, and number of turns around the rod. In purple, we found the units of Inductance from the formula V = LdI/dt.

We did another series of questions on the same website. This time we found the relationship between induced emf, current, time, and the magnetic flux.

We made our graphs of time versus current and time versus voltage where there is an inductor in the circuit. On the bottom, we predicted that current would eventually reach a limit. On the top, we found that the actual graph for current is that the current would automatically reach its peak when after a certain period of time because the inductor resists the immediate change of voltage. So its basically the bottom graph except with the first half missing.