6/2 RC AC Curcuits

In todays class we explored AC RC and LRC circuits. In DC circuits, ohm's law is applied. In a AC circuit the same law applies, the only difference is that capacitors, resistors and inductors create resistance.

We began by defining a few formulas such as root mean square current, root mean square voltage,  capacitance reactance, inductive reactance, and impedance.

we began our first experiment by connecting the function generator across the resistor and capacitor with a current probe across the resistor and capacitor. 

We then started Logger Pro and connected the sensors. We measured Voltage and current. Using the stats button we got our values for maximum voltage and maximum current. We were given different frequency which we used to conduct the experiment.

Here is a close up of our values for Vmax and I max.

Here we have our second frequency.

and our second set of values for Vmax and Imax.

Using Vmax and Imax we were able to calculate experimental impedance. We then compared it to the theoretical impedance. For 10hertz, our theoretical impedance was 159.3 ohms and our experimental was 153.5 ohms with a 3.64 % error. The percentage is reasonable. For 1000 hertz, the theoretical impedance was 10.13 ohms and the experimental was 32.9 with a 224.8% error. This error was high because there must have been some inconsistency with the wiring or procedure. We also used the incorrect frequency with could've been a major factor in the high percent error. 

We also computed the phase angle using the formula above (inverse tangent *inductance reactance minus capacitance reactance divided by resistance).
In conclusion,  When frequency is low, the impedance of the capacitor is high, so most current will flow through the resistor. As the frequency increases, more current is diverted through the capacitor, and less to the rest of the circuit. Thus, the response is low pass.

5/28 AC Circuits

In today's class, we examined AC circuits and how capacitors, inductors and resistors behave with this type of power supply.

We began class by calculating root mean square voltage of a oscillating voltage with Vmax.

Alternating current with a resistor

In our first experiment, we use logger pro to graph current and voltage using an AC power supply with a resistor. The graph that is produced is sinusoidal. From here we can get our Vmax value. 

After finding the slope of the current, we found that the average current is zero.

Using the graph from logger pro, we were able to get Vmax and Imax so that we could calculate root mean square voltage. 

Alternating current with a capacitor

Here we derived the formula for voltage with capacitance and we see that there is a phase shift.

In this experiment, we connect the AC power supply to a capacitor and measure the voltage and current using logger pro. We found that when there is a large voltage across the capacitor it is indicating that the capacitor is fully charged. We see that current is zero when the voltage is at its maximum.

Here we have our voltage vs current graph, which formed a circle. This indicates the motion of the current when it is at a certain voltage, and indicated that power is conserved because of the capacitor.

Using our graphs from above we calculated reactant capacitance using Vrms and Irms. We calculate the experimental and theoretical then compared both. We had a 79% error which is really high, this is because we did not account for the resistance within the power supply. We also calculated the phase shift and found it to be 0.23.

Alternating current with inductors

For our next experiment, we connected the AC power supply to an inductor in order to see how its behavior. 

Here we derived the formula for inductive reactance, which is equal to omega times inductance.

Here we have our graph of current vs. voltage, we see that the graph is consistent with the phase shift 

Using our graph from logger pro we were able to calculate the experimental value of capacitance reactance and compare it to the theoretical value. We  got a 25% error. We also calculate the phase shift which ended up to be 0.35.