28th of May's Class
We started the day learning about the AC circuit and a variant of the Voltage formula that utilizes omega, time and phi. Also learnt about the Current variant of it. Note that in this form, there is no negative value for either variable. We were also refreshed about omega, the circular velocity, which is defined by 2 * pi * frequency.
We were then taught of the existence of V(rms) and I(rms). In DC circuit, the values of voltage and current will remain constant. However in AC circuits, there is an alternating current flowing, therefore they do not remain constant, but oscillate between certain sets of values. The average value found for voltage and current values respectively is called the root mean square version of them.
As a practice, Professor Mason gave us a question regarding the voltage of the wall socket. The voltage was commonly known as being in the value of 120V. However, we were brought to the understanding that that value is actually the root mean square of voltage and not its peak, or its maximum. So to calculate the maximum voltage that the wall socket would give out, we use the formula for finding the root mean square voltage. We multiply both sides of the equation with square root of 2 to get the maximum voltage output by the socket.
Next, we experimented with a new board which already contain capacitors and resistors on it, it looked like this:
(Bordered in Green)
We used a function generator as the power supply for the circuit. Setting the frequency to 10Hz, and the voltage to 3.00V.
The set up is as shown in the drawn diagram below, with a slight error. The voltage probe should have been in parallel with the resistor.
With the probes connected to the LoggerPro, we graph out the values on the computer which looked like this:
From the graphs, we can obtain the reading of their peaks. Meaning, the V max and I max. We can also obtain the Phase Shift by finding the difference in time of the peak of current and voltage, then dividing that value by the period.
The image above is the record of the experiment we did. The maximum current and voltage were obtained by finding the peaks of their respective graphs (written in Purple). Their root mean square values are written in Orange determined by multimeter (shown below). We also derived their theoretical root mean square (written in Purple at the upper half of the white board) to compare and calculate the percent error written in Pink.
Written in Red is the formula derived for finding the Current in AC circuit as a function of time. the resulting C * omega is the multiplication factor that differentiates the amplitude of Current and Voltage.
Although we did not take a picture of a graph created from the current and voltage, it should result in a straight line in the form of y=x. The slope generated by the graph is the Resistance of the resistor that we hooked up to the system.
This is the resultant graph when we put both Current vs. Time and Voltage vs. Time in the same plane. They have similar shapes and movements, but they have different amplitudes and phase shifts. The phase shift can be calculated by finding the difference in the time for both graphs to reach their peaks and dividing that value by the period.
The image above shows the different variables that are frequently involved in AC circuit calculation, with an inductor present. An important variable that is introduced is 'chi', which is written in the form quite similar to an 'x'. It functions similarly to Resistance, as one of its forms is 'chi' equals to root mean square voltage divided by root mean square current. It is also the inverse of "capacitance multiplied by angular velocity". Observing these equations, we learn that unlike capacitors, which remain unaffected when there is a change in frequency, Inductors are affected by the changes in frequency.
Next, we repeated the experiment that we did earlier. However, we do not hook it up to a resistor. Instead, we hook it up to a capacitor. The capacitor is shown in yellow box within the image below:
The image above is the record for the values we obtained from the experiment. With the same method for gathering data, the maximum for Current and Voltage is obtained from LoggerPro, while their Root Mean Square counterpart is obtained from probes. In this exercise we learnt the practical usage of finding the phase difference. It is found by looking at the time difference between the peaks of Voltage and Current, then dividing that value by the period of the wave.
Next, we repeated the experiment again, but this time it will be hooked up to an inductor (shown right below) instead of capacitor:
We tweaked a bit with the conditions of the experiment, like the voltage supply this time gives only 0.5V instead of the usual 2.0V. Chi is obtained by its simpler version, which is the Root Mean Square of Voltage divided by the Root Mean Square of the Current.
Lastly, we were introduced to the concept of Impedence, symbolized with a 'Z', much like the 'Chi' functions similarly to Resistance, the summary is in the next image:
We were supposed to have compared our finding for the experimentally determined Inductance for this inductor that we used this day. However, our data did not match our calculations from the previous lesson. This we assumed to be due to the faulty Inductor we used last lesson (which was mentioned in the previous blog entry). It might have been replaced or gave out an eccentric value, so we cannot be certain.
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