5/28 Alternating Current (AC)

We solved for the formula to calculate the root-mean-square value for current and voltage.

We setup an experiment to calculate the RMS values for current and voltage using the function generator to produce a constant voltage and a closed circuit provided. We used a voltage meter and used logger pro to find our rms value for the voltage.

We took values from our graphs in logger pro to calculate the RMS for voltage and current. We know our max voltage is slightly less than the one indicated on the function generator and took that into consideration when calculating for our RMS of voltage. We found that our experimental value for the RMS of voltage is exactly the same as our theoretical value. We then found the current and noticed that there was a small difference between our theoretical and experimental values. We then drew the graphs of voltage, current, and voltage and current superimposed vs time. We found that the voltage and current, when superimposed make the positive x-axis.

We used the RMS of voltage and current and derived an equation to solve for the capacitor reactance. We then used what we derived here to solve a problem with the given values on the top right corner. We then used this derived formula on our next experiment.

We repeated the same experiment but included a capacitor. We found 3 RMS values for current, 1 from the graph in logger pro, another from calculations, and another from reading the voltmeter. We found that all 3 values varied slightly from each other but are within margin of error. We then found the phase change between the graphs we had of potential and current. Note: The phase change we calculated for in this experiment is incorrect. Instead of adding we should have subtracted.

From our previous experiments, we found that electric potential is a sine graph and current is a cosine graph. From this, we determined that current must be a function relating to cosine and electric potential must relate to sine and we derived their respective equations on the left. On the right, we took given values from a problem in class that would use our derived formulas to find the RMS of current.

We repeated our experiment once more, this time comparing the RMS values of electric potential. For our theoretical values, we found that our inductance value was off because the original percent error was too great. Instead of calculating for the RMS of electric potential, we instead found the correct inductance value. Because we used the value from the graph, our experimental value and theoretical value for voltage are the same hence the 0% error. The formulas we used and the givens are written in dark blue on the left. We also calculated for phase change on the bottom right.