5/28 week 14 day 2 Resistors, Capacitors, and Inductors in an AC Circuit

Alternating Currents and Voltages

At the beginning of the class, the professor shows us the graphs of alternating currents and voltgaes. They are both Formulas of trigonometric functions. And we know that the relationship between V_max and V_rms, I_max and I_rms are V_max=square root 2 *V_rms, and I_max= square root 2*I_rms.

In this photo, there are the relationships between  V_max and V_rms, I_max and I_rms. We look at the oscillating voltage of an AC power supply. We calculated the Vrms in relationship to Vmax in the calculations using integration shown in the photo

Then we did an example which is at the bottom of this photo.

Then we use a circuit board we preformed three experiments using an AC power supply across a resistor, capacitor, and inductor where we used logger pro to analyze the current and voltage.We have that V_rms=120V and find that V_max is 170V and the perk to perk is 340V.

Then we did an experiment about alternating currents and voltages. We use vernier logger pro current probes dual channel amplifiers, function generator, resistor using the RLC circuit board and a digital multimeter and sevearl wires.

In this photo, we connect all the equipment and use the logger pro to find the graph of alternating current and voltage.

There is the graphs of alternating current and voltage. The red one is current and the blue one is voltage. The graph shows that as voltage increases, current also increases as seen in our sinusoidal graph and fit. Most importantly, the graph shows that the voltage and current is in phase with each other.

We set up the resistor is 100 omh and voltage is 2V, and use the graph to find the V_max and I _max and use the equation V_max=square root 2 *V_rms, and I_max= square root 2*I_rms. to find the V_rms and I_rms.  and use 2V and 100omh to find the theoretical V_rms and I_rms and find the error of them.

Capaitors in a AC Circuit

We know the equaition of V=V_max*sin(wt+theta) and we use this equaiton to find the equation of I and we find that the aptitude of I is bigger than V,.We derived another set of equations with capacitance and found that there is a phase shift. Since we know that the angular frequency is 2pif. 

In this photo, the professor gives us that C=0.02uF and f=10kHz and V_rms=50V . We can calculate the capacative reactance with the given frequency and capacitance then apply ohms law to find the Irms using the Vrms value.we know that the equation about X=1/wC and w=2pi*f so we get that X=796 and I_rms=V_rms/X and we get I_rms=0.063A

Then we diid an experiment about Capacitors in an AC circuit.
We use a vernier Logger pro voleage probe current probe dual channel amplifier, one function generator and RLC circuit boad to do this. we set up for frequency=100Hz, the indicated is 100uF, and the voltage is 2V.

Then we connect the equipments and use logger pro to find the graph of I and V. Then accodring to graphs, we find the V_max=2.005 V and I_max= 0.116A The graph shows the current and voltage with an capacitor with results indicating that the voltage graph is lagging by 90 degrees meaning that they are out of phase. This is consistent with our derivations. When there is a large voltage across a capacitor, that means the capacitor is fully charged Q=CV. 

Then we filled the form in these two graphs by using the same way to do the experiment of Alternating currents and voltages.When Q is max, we get that the capacitor will impede the flow of charge. Therefore the current will be zero when voltage is at maximum and minimum seen in the graph. When the voltage goes negative, it will induce a current causing the current to be at a maximum. and we get that I_rms=0.0731A,V_rms=1.42V and the theoretical capacitive reactance is 15.9. and the experimental capacitive reactance is 19.4 so the percent error is 18%.

In this photo, in order to make sure we did right, so we use the equations to find the I_rms is 0.089  is almost like the I_rms we find by using data from the graph.

Inductors in Alternating Circuits

In this photo, according the equation V=V_max*sin(wt+theta), use the intergel to find that I=-V_max/wL*cos(wt+theta)

The professor give us that V=0.5V, L=0.5uH, f=100Hz and we use the equation X_L=wL to find that X_L=3.14*10^(-4) and I_rm=1126A, which is very large.

Then we begin to do the experiment about inductors in alternating circuits.
we use the same equipments but just change capacitor to inductor.

we use a N=110 inductor to find the L=uN^2A/l= 7.6*10^(-8) and find that X_L=wL=0.48.

Then we use logger pro to make this graph in the photo, and do the same thing like find the V_rms, V_max, I_rms and I_max.The results showed an interesting elliptical shape for the current vs voltage graph and this is consistent as the phase shift is under 90 degrees in comparison to the capacitor

we use the datas we find to fill this form. We summarized the results of inductors in AC circuits and we found that we ran a current through using a function generator, collected data, calculated expected values for I(rms) and V(rms) using our data, and then took actual readings using a multimeter. Our values (seen below) are slightly better in regards to the percent error, but the error is still rather high.

Conclusion:

Today in class, we created three circuits which consisted of a function generator and one of preformed three experiments, which were a resistor, capacitor, and inductor. We learned a lot on thursday about RL and RC circuits and the graphs that are generated from the RL and RC circuits. By relating Vmax and Imax values, we can find our Vrms and Irms in order to analyze our results. We saw how the phase shift affects the graphs and calculated it to be t(time)/T(Period)