AC on Capacitors and Inductors

Alternating Current on Capacitors and Inductors

After connecting a function generator to a 220E-6 F capacitor and setting up LoggerPro for voltage and current data collection, we made some initial calculations.

We calculated the reactance of the capacitor (X_c) at a frequency of 10 Hz to be 72.34 ohms. The calculation is shown above under the "theoretical" heading. Next we turned the frequency on the function generator to 10 Hz and collected the data on LoggerPro.

From the sinusoidal current and potential graphs, we obtained the maximum voltage (V_max) and maximum current (I_max). [Unfortunately the screenshot above does not explicitly show how we obtained the values. The next trial shows in detail how we obtained our data].
We calculated the experimental reactance ("exp") using the formula shown above. The reactance is the ration of the root mean square voltage (V_rms) divided by the root mean square current (I_rms). V_rms is equal to V_max divided by sqrt(2) and similarly, I_rms is equal to I_max divided by sqrt(2). We then clean up the equation to get an equation we can use with our measured values, X_c = V_max/I_max. We plugged in our "max's" to this equation and found the experimental reactance to be 69.69 ohms. When we compared this value to our theoretical value, we got a 4% error.

We repeated the calculations for a frequency of 20 Hz. We found the theoretical reactance to be 36.17 ohms. Above we see the collection from LoggerPro with greater detail. 

For our experimental values we used highlighted a part of the graph and used the "Statistics" option in LoggerPro. A box in each graph shows the maximum potential (V_max) and maximum current (I_max). We saw that V_max = 3.21 V and I_max = 0.08862 A. From this we calculated X_c = V_max/I_max = (3.21 V)/(0.08862 A) = 36.22 ohms. Compared to the theoretical value 36.17 ohms, there is a 0.1% error.

Now we connected an inductor of an unknown inductance. We used the formula below to calculate the inductance of the inductor. Again we used LoggerPro data to find V_max and I_max. We saw that we could take various trials at different frequencies and compare the experimental values for inductance to find the inductor's inductance We did this for 10, 20 and 40 Hz, respectively and found that the values averaged 1.32 H.

We repeated the experiment with a bolt inserted in the center of the inductor. We calculated the values for inductance the same way we did the first time and found that it lowered significantly.