Lab 25: AC RC and RLC Circuits

At the beginning of the class, professor Mason start explaining that Ohm's law also applies in AC circuits, as it does in DC circuits. The difference is that in AC circuit there are three resistance, created by resistors, capacitors and inductors. This total resistance is called impedance, categorized by the letter Z. In RC circuits, the Z = sqrt(R^2+XC^2). 

 We know that Vrms = ZIrms from Ohm's law, and that XC= 1/ωC, we solve for Irms, and found out that if the angular frequency doubles it causes the root mean square current to double.

 Here is the set up of RC Circuit in AC. We used the RLC Circuit board, we connected a resistor and capacitor to the function generator, and the voltmeter and current sensor to logger pro. In logger pro, we zero out both sensors, and set the sampling rate at 5000 with a frequency of 10Hz. And graphed the V vs T, and I vs T.

 We used 100 ohm resistor and 100μF capacitor, we found Vmax and Imax by looking at the graphs. Then impedance was calculated through the formula Z = Vrms/Irms. Our percent error was 0.6%. We also found the phase change between the V(t) and I(t) to be -1.5 rad by using ϕ = arctan(-XC/R). We also did the experiment with a frequency of 1000Hz, for this case, logger pro does not allow high sampling per second when two sensors are connected at the same time, so we disconnect and record the samplings with only one sensor because logger pro can sample up to 50000 per second, our percent error turn out to be 1310%, a really big error. Finally, we repeated the experiment one more time with a frequency of 100Hz. And found that the phase change was -1.00 rad.

 In this photo we calculated the experimental phase change.

We started working on Resonance in RLC circuit lab. In RLC, Z = sqrt(R^2 + (XL - XC)^2). When the impedance is minimized the current is maximize, for this reason there exists a frequency called resonance frequency, it occurs when f = 1/(2pi(sqrt(LC))).

 We calculated the resonance frequency of the given circuit to be 5033Hz. Then we used a resonance frequency of 3kHz, we calculated the capacitive reactance and inductive reactance. With these values, we were able to compute the value of Irms in order to calculate the power dissipated by the resistor using P = Irms^2*R.

 For this experiment, we used the RLC circuit board, inductor, function generator and a multimeter. The goal was to measure the resonance frequency at which maximum current occurs. We used previous values when we used a 55 turn inductor. The inductance calculated was 324μH and the capacitance was 470μF, with these values the resonance frequency is 408Hz.

The theoretical impedance is Z = R, and for the experimental impedance we used Vrms and Irms.