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.

5/14 Faraday's Law and Magnetic Force

Professor Mason uses a Halls Effect sensor to find the magnetic field inside the classroom. When he spun around the classroom for the 10 seconds Logger Pro took data for, it showed a sinusoidal behavior. This is because when mason spins basically spinning a compass around and the needle's behavior is what we observe on the graph. 

We made a copper coil and used the same sensor used to measure the magnetic field of a coil of 1 loop of wire up to 5 loops of wire. Our measured magnetic field is shown as this graph

We drew a current going down 2 wires that are in parallel and were asked to find the force vector created by their magnetic fields. We found that with the right hand rule, the force cancels in the middle and goes in through the board on the left and out through the board on the right.

 

In these two pictures, Professor Mason uses an ancient device to measure the magnetic field when moving a metal rod at inside a coil of wires. We observed that when there was no movement, there was no magnetic field. 

In the above 4 pictures, we created a magnetic field that would induce a magnetic field on the object we placed around it. We tried this with 3 different types of material, wood, copper, metal. We observed that with a wooden ring, nothing would happen. The wood is not a conductor therefore there is no way for the current to travel through it. We then tried copper, a very poor conductor. We found that the copper ring jumped a bit but because it does not conduct the current well, it only did a small jump. We then tried 2 different metal rings, one thin and one thick. The thick one jumped up a bit and stayed floating. The thin one flew off the tube. Because metal is such a good conductor, it was able to conduct a high enough current to create a magnetic force in the downward direction. The thin metal ring flew off because it was just as good of a conductor but was lighter so the magnetic force larger.

We calculated the flux of 2 plates oriented differently. The flux from the magnetic field when plate is parallel to the magnetic field is 0 and the magnetic field when the plate is perpendicular to the magnetic field is the magnetic field times area. The actual formula is the dot product of the magnetic field and the area. We were then asked what elements could change the magnetic field. From our experiments, we answered the 4 in orange. 

We have 2 tubes, one aluminum tube and one acrylic tube. This experiment was to see what would happen if a magnetic object was dropped through the acrylic tube and the aluminum tube.

This is our results from the previous experiment. We found that when the magnetic object was dropped through the aluminum tube, it went through significantly slower than it did through the acrylic tube. Even though aluminum is a poor conductor, it still managed to create a large enough magnetic force from the magnetic object's velocity to slow it down significantly. We then derived its relationship.  

The top graph shows a magnetic field graph vs. time and the bottom graph shows an emf graph over time. We found them to be sinusoidal. If we were to interpose the graphs, we would get the x-axis. 

5/12 The Magnetic Field of a Current

Professor Mason used a magnetized paper clip to demonstrate how a piece of metal loses its magnetic field when its heated. Heating the molecules causes the poles to realign themselves back to before they were magnetized.

On the right, we have pictures of how the poles on a piece of metal are aligned when they are magnetized and when they are not magnetized. The magnetized piece of metal had all their poles aligned so that the north and south poles were pointing in the same direction. The non-magnetized one has poles pointing in all directions so the poles magnetic field cancels each other out. We were then asked how we could destroy the de-magnetize the magnetized metal. We said that if you hit it really hard or heat it up really hot, it would realign the poles back to pointing in all directions.

This is the sample motor that Professor Mason gave to each group. We noticed that for the coil to spin fast, it had to be as close as possible to the magnets on each side. They were so close that you could notice scratches on the magnet. We also noticed that it is better to have a north and south pole magnet on opposite sides of the coil to keep the coil spinning fast.

This is our motor created with a coiled piece of wire, batteries, a magnet, and a closed circuit. We found that the most difficult part of having the engine run consistently was to have the coil as close as possible to the magnet underneath it. This way we can shorten the time that the coil is in the part of the spin where there is no torque, and the momentum can easily push it to keep spinning. We also found that if we have bends on the ends of the wire, it would cause a torque in the direction of the bend causing the coil to not spin smoothly. Straightening them made it spin smoother but made it easier to fall out.

We discussed the different components that are required for a motor to run. We found that the thing that is most likely to break in a motor is the brushes as they are made out of thin plastic and are frequently used to change the direction of the motor.

The above 2 pictures are from an experiment we did if we had a current going through the metal pole in the center of a box surrounded by compasses. We found that the current produces a magnetic field causing the magnets to point in a counter-clockwise direction around the metal pole. This matches our right hand rule along a current.

This is a problem we did in class of a current going through the pattern shown above. We were asked to find the force in between the wires at the very top. We found that with the right-hand rule, the magnetic field caused by the current is going through the circuit at that point is going into the board.

We drew our predictions for the compass experiment as well as the force between the wires at the very top. From these 2 experiments, we derived equations that related the magnetic force and the force due to the electric field.