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.