University of Arkansas System
Type of paper: Thesis/Dissertation Chapter
In the experiment AC circuits, the purpose was to see the effect that a capacitor, resistor, and inductor have on the voltage, and current of a circuit. We created circuits with 2 resistors, a capacitor and a resistor, and then a capacitor, resistor, and an inductor. The circuits were then hooked up to a function generator, and oscilloscope to find the voltage across certain frequencies and then calculate the peak current, capacitive reactance or the inductive reactance, and phase difference.
When beginning the experiment, we measured the resistance of both resistors with a digital multi-meter and received values for R1 as 559 Ω +or- 10 Ω and for R2 as 108 Ω +or- 10 Ω. After measuring the resistance, we placed each of them in series on a circuit board and we increased the frequency four different times ranging from 100 Hz to 5,000Hz and measured the voltage across each resistor and determined the phase relationship. We then replaced the 559 Ω resistor with a 1μF capacitor, where we performed a similar process, only this time we increased the frequency eight times, ranging from 100 Hz to 5,000 Hz measuring the voltage across the capacitor and resistor, and finding the value for Δ t.
We then calculated the peak current, capacitive reactance, and phase difference, and then graphed the reactive capacitance vs. the period to get a slope (3731.3) and then determine an experimental value for the capacitance (4.2654*10^-5 F) where we then calculated the percent difference (96.52%). Next, we replaced the capacitor with an inductor, repeated the same process, except rather than measuring capacitive reactance, we measured inductive reactance, and then plotted inductive reactance vs. the frequency and used the slope (.0185) to calculate the value for L (.0306). Next, we added the capacitor back into circuit, aligning them all in series where we repeated the process finding the voltages across the inductor, capacitor, and resistor, then graphed the current vs. the frequency. I then went back and determined the percent difference between the resonant frequency based on theory (8926.766 Hz) and the experimental resonant frequency (1374.9259 Hz) and got a value of 146.614%.
In regards to the error, the majority came from the possibility that our circuit was improperly set up, causing to the current to essentially bypass the resistors. Part of the discrepancies in the percent difference with the capacitance is because the manufacturers staple a 20% uncertainty to the1μF capacitor, as for the rest of the percent difference; I again contribute it to a flaw in our circuit set up. In determining the experimental value for the resonant frequency, we derived this value from using information from the graphs. I believe if our graphs had been more accurate, it would have resulted in a much more accurate value that lays closer to the theoretical value. Another possibility for error is that inductors have their own resistances that we ignore for the sake of simplicity. The added resistance from the inductor was not factored into any of our measurements. Also, it should be noted error might stem from imperfect scope readings.
Knowledge gained from this lab will allow me to approach circuits much more thoroughly and build conclusions from very little provided information. For instance if I came across an AC circuit that had a 500 Hz frequency and that had a resistor and EITHER a capacitor OR an inductor, I would be able to determine the remaining component from information about the voltage in different places. If the voltage across the circuit leads the voltage across the resistor, I would know that the remaining component is an inductor. Likewise, if the circuit voltage lags the resistor voltage, I would know that the remaining component is a capacitor. However if the circuit could have a capacitor AND an inductor, I would require more information in order to determine the circuit’s composition.