Professor Mason
Physics 4B
May 28 Class
Graph and Properties of AC Circuit
The first thing we learned in class was about the properties of AC circuit, as well as the Voltage vs Time graph and Current vs Time graph. In class, professor Mason showed us the form of Voltage vs Time graph in AC circuit, and it is shown in the picture attached on the left; he also showed us the form of Current vs Time graph in AC circuit; the difference between those two graphs is that Voltage vs Time graph has higher amplitude than Current vs Time graph (NOTE: the graph in the picture on the left is wrong, the top one should be I vs t, and the lower one should be V vs t because V vs t graph has higher amplitude than I vs t graph; they should be swapped). We also learned the properties of AC circuit in class, and one of those is the Voltage across resistors, which has an equation of [V = Vmax Sin(2 pi f t)] or [V = Vmax Sin(wt+flux) + Vo], and [w = 2 pi f = 2 pi/T]. We also found out an equation of current across resistors, which is [I = Imax Sin(wt + flux) - Io]. Professor told us an average value of V vs t graph (sin graph) is equal to zero; however, if this sin graph was squared, the graph becomes like the graph shown in the picture attached on the left [V=Vmax sin (2 pi/T)t]. The average value of sin squared equation is equal to cos squared equation value. We also found out that Irms and Vrms has equations of [Irms = Imax/2^1/2] and [Vrms = Vmax/2^1/2]. In class, we also learned that Average Power has an equation of [Pavg = 1/2 I^2max R], so that [Vrms = Irms R].
After we finished learning the properties of AC Circuit in class, we continued to the experiment. This experiment's setup contains current sensor parallel to a 100 Ohm resistor, Voltage probe, function generator, and motion detector connected to logger pro. We first needed to set the frequency and voltage in function generator to 10 Hz and 3 V.
The pictures attached on the left shows how we set up the circuit, and the graph picture on the left shows us how the Current vs Time and Voltage vs Time graph would look like after we hit "Collect" button on Logger Pro based on our circuit setup. Next, we needed to find the Vmax and Imax from the graph to calculate the experimented Vrms and Irms.
After we got the graph, we needed to compare the theoretical Vrms and Irms measured from the multi meter with the experimented Vrms and Irms from the graph. They turned out to be almost the same, and the percent error turned out to be 36.4% for Irms and 1.45 % for Vrms shown in the picture attached on the right.
After we finished the experiment, we figured out a new equation, which was [Q = Integral of I dt], which would equal to [I = C dv/dt]. Based on this experiment, we also found out that Current as a function of time across capacitor has an equation of [I(t) = C Vmax w cos(wt+flux)]. The difference in amplitude in graph from V has a difference by I(t) = C w.
Capacitive and Inductive Reactance
After we finished the calculation based on the experiment above, we continued to phase difference and Capacitive reactance and Inductive Reactance. We were given an equation of phase difference, which is [Phase diff = delta t/T], which would be used later on the next experiment. We also found out an equation of capacitive reactance, which is [Xc = 1/ cw] or [Xc = 1/2 pi f c], and also can be [Xc = Vrms/Irms], which Xc has a unit of Ohm. On the other hand, inductive reactance has an equation of [Xl = wL] or [Xl = 2 pi f L].
In this experiment, we had the exact setup and steps as the experiment with 100 Ohm resistors; the only difference is we were using 100 uF capacitor instead of resistor. The picture on the left shows us how we set up the circuit for this experiment. After we hit "Collect" button, it would show up a graph like shown in the picture on the left. The calculated Vmax, Imax, Experimented Vrms and Irms, Theoretical Vrms and Irms are shown in the picture attached below, as well as the percent error.
This time, we needed to find the phase difference, which is the time difference between v vs t graph reach first max point and I vs t graph reach first max point divided by period; we got 0.24 as the phase difference.
RMS and AC Current and Voltage Experiment
The pictures attached on the left shows how we set up the circuit, and the graph picture on the left shows us how the Current vs Time and Voltage vs Time graph would look like after we hit "Collect" button on Logger Pro based on our circuit setup. Next, we needed to find the Vmax and Imax from the graph to calculate the experimented Vrms and Irms.
After we got the graph, we needed to compare the theoretical Vrms and Irms measured from the multi meter with the experimented Vrms and Irms from the graph. They turned out to be almost the same, and the percent error turned out to be 36.4% for Irms and 1.45 % for Vrms shown in the picture attached on the right.
After we finished the experiment, we figured out a new equation, which was [Q = Integral of I dt], which would equal to [I = C dv/dt]. Based on this experiment, we also found out that Current as a function of time across capacitor has an equation of [I(t) = C Vmax w cos(wt+flux)]. The difference in amplitude in graph from V has a difference by I(t) = C w.
Capacitive and Inductive Reactance
Experiment with 100 uF capacitor
Experiment with Coil
This last experiment today was also the same as the other two experiments; however, the only difference is we used coil instead of resistor of capacitor. This time, we needed to compare this result with the previous result on previous meeting. The graph looks like this, shown in the picture attached above, when it is connected to motion detector, function generator, and probe in Logger Pro.
Phase Angle and Impedance
The last thing we learned from today's class was the formula of phase angle and impedance. Phase angle has an equation of [tan (theta) = Xl - Xc/R], while impedance has an equation of [Z = square root of R^2 + (Xl - Xc)^2], which theta is the angle for phase angle, and Z is the impedance. 
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