RLC Circuits in AC cont.

The day began with a little surprise for us early birds. Professor Mason gave us an idea of what was going to be on the final exam. Pretty much what is shown below is what the exam would cover and we also went over V (rms) and I (rms) again but this time involving the variable Z which equal root (R^2 * Xc^2) and then we solved for I (rms) by itself and substituting 1 / 4*omega^2*C^2 for Xc^2.

We then did some more activities involving RLC circuits as shown in the graphs below showing Current vs Time and Voltage vs Time.

We also did a cosine fit for both of the graphs since both were AC circuits and the voltage and current oscillates until it reaches a maximum and minimum value.

Using the graphs shown above we were able to finish the table shown below recording what would happen to the flux if the frequency was increased so we tried the experiment with 3 different frequencies which were 10 Hz, 100 Hz and 1000 Hz. We compared the values from the theoretical values and got high error percentages but it was probably because Mason guestimated again.

We then moved on to an ideal AC circuit problem having a resistor, capacitor and inductor. We were asked to find the frequency, the current value and the average power of the circuit.

We ended the class by having to find the frequency of another one of the RLC circuits. Our calculations are shown below.

Overall, the class dealt with the final part of the RLC circuits in AC and solving some more simple problems involving these different values.

AC and RLC Circuits

The day began with an introduction to AC circuits and RLC circuits and finding how current and voltage behave throughout using Logger Pro. The result of the graph we acquired is shown below.

The introduction to AC circuits are shown below on how we get the root mean square voltage and how it can be used to solve for the voltage needed in an AC circuit.

The set up of how the R circuit in AC looked like is shown below.

Using the information about AC circuits that we had just learned and using the graph from Logger Pro, we were able to find the needed values to fill in the table below.

We then moved on to the behavior of the voltage and current in a perfect AC circuit as shown in the hand-drawn graph below. We also did some more calculations regarding root mean square values of current and voltage.

We then moved on to a circuit in AC involving a capacitor. The graph of what the voltage and current looked like is shown below. The set up was pretty much the same as an R circuit in AC but with a capacitor hooked up.

The results from our data is shown below.

We also did some more problems with AC circuits  involving frequency, inductance and finding the value of X sub L.

We finally moved on to a complete RLC circuit within AC. The table of our values are shown below.

The set up shown below included everything connected in series.

The graph from Logger Pro is also shown below and shows how the current and voltage still oscillate when in AC.

Overall, the main focus of the class was to see how the current and voltage behaved in AC and how putting each of the components including capacitors, resistors and inductors affect the outcome of the voltage and current.

Inductance Continued and Current Flow Time in an Inductor

The day began with an ActivPhysics activity 14.1 called The RL Circuit. It was a circuit with resistors and inductors. We began solving some problems until Mason told us to stop because he thought we had done it before (which I do not think so) and so we moved on to another RL circuit which dealt with a closed circuit involving resistors and inductors with a switch and a 45 V battery. We solved for the torque of the inductor, voltage and current at the different points of the resistors and inductors. We also talked about how long the inductors would take in order to charge fully and how long they would take to charge to a certain point.

Using a previous 110 turn inductor (for which we calculated the inductance of) we tried to see whether our measurements could result in almost the exact amount of turns which it did not as seen below because we assumed many of the variables (which we always do haha).

Below is a picture of the set up we had in order to measure the current output made by the function generator and the closed circuit shown in the next picture. The waves indicate that the current reaches a certain point and then it it looses charge and then it repeats but I do not believe we got the correct function.

Below is a picture of our set up and how we connected the whole thing in series except for the resistor because that was in parallel with the inductor.

After Mason helped us out, the function shown below is what the actual outcome should be showing that as current goes through the charge reaches a maximum point and then resets every time a current goes through.

Below is a picture of the new set up that actually worked for us.

Next we talked about inductance and solved some more problems regarding inductance involving finding certain variables like resistance, inductance and the period of it.

Overall, the main emphasis of the day was to sharpen our skills regarding inductance and also the time it took for an inductor to reach max capacity.

Change in Direction of a Magnetic Field and Inductance

The day began with an ActivPhysics activity regarding magnetic fields and what increasing or decreasing variables would do to the overall results. We played around with a little graph where we changed the variables as well and we saw how the graphs of magnetism and force changed as we also increased or decreased variables.

Professor Mason then showed us what would happen to a magnet if current was turned on within the rod found in the picture below. He made us guess whether it was going to roll away or towards the magnet if the direction of the current was changed.

Below is a picture where Professor Mason asked us to predict how the force, magnetic field and current were behaving in the model above. Our results are shown in the picture below.

We then did another ActivPhysics activity regarding magnetic flux and how current direction affects the outcome of the magnetic field. We also related the flux between electric field and the change of area is equal to the charge over the constant epsilon not. We related that equation to the magnetic force one and found that the charge times the electric field plus the charge times the speed cross the magnetic field.

We then moved on to the topic of inductance defined by the symbol L. We found that the equation for inductance is mu not times the number of turns squared times the area all over the height of the coil.

We also solved an inductance problem within a closed circuit and was able to find the potential of the inductor.

Lastly, we did another ActivPhysics activity and then we decided to call it a day.

Overall, the main focus of the day was how the direction of the current affects the magnetic field and we also learned about inductance and inductors as well.