AC Lab

In this lab assignment, unlike in previous lab assignments, we performed an experiment with an AC source. Our objective was to analyze an an inductor with an inductive resistance in series, for which its impedance is given as Z = R + XLj.

Our first step was to determine the inductive resistance using a digital multimeter. We came up with a resistance of 3.2 ohms.

Step 2 required us to determine the inductance. In order to protect the function generation or the inductor from possible damage, we were instructed to create a test circuit shown below.

The resistor Rext in the photo above was the resistor we used to limit the drawn current. We were asked to use a theoretical value of Rext = 68 ohm. After choosing the appropriate resistors, we measured them with a multimeter and they came out to a total of 68.8 ohms.  Next we were to set up the function generator by energizing it and setting its frequency to 20.0 kHz and setting the RMS value to 5.00. We then energized the multimeter and connected it to the function generator. We achieved an experimental result of 4.91 ohm.

As shown in the photo above, we were required to build the circuit on the breadboard. We then took measurements of V in,rms and I in,rms which turned out to be 4.63 V and 69.1 mA, respectively. We were told that our V in,rms value should be less than 5.00 which indeed was the case. We did notice a difference in the voltage reading as compared to the function generator reading. We hypothesized that the internal resistance of the ammeter was the reason for the ammeter. Next, we were required to measure the corresponding value of the impedance from the above measurements. Here is what we obtained:

Next, we were required to rewrite the expression for the imput impedance. Here is what we obtained:

After that, we were asked to compute the magnitude of this impedance:

Then, we computed the angular frequency:

Finally, we used the equation the magnitude of the impedance in order to compute the value of the inductance:

Now we were ready to move on to Step 3 and analyze the following circuit below:.

To start off we were asked to compute the value of the capacitor using the values of the angular frequency and the inductor. Here is what we obtained:

Next we were required to set the capacitor box equal to this value and to modify the circuit to it's required values:

We were now to include the oscilloscope. After energizing it, we connected CH1 across the multimeter and CH2 to the inductor. After calibrating the oscilloscope, we obtained two cycles of a sinusoidal wave.

Setting the oscilloscope to a frequency of 20.0 kHz, we made the following measurements for Vpp,CH1, Vpp,CH2, and delta t:

The phase angle was computed to be 90 degrees out of phase.

Next, we were instructed to record the multimeter measurements for some selected frequencies. Here is what we obtained:

The laboratory procedures were now done with. We were now asked to answer some followup questions.

1.  The current is at it's highest value at 20.0 kHz because of resonance. The inductive and capacitive reactances cancel out and the circuit is the purely resistive.

2. The circuit looks more inductive at frequencies above 20.0 kHa because angular frequencies are directly proportional to inductive reactances.

3. The circuit looks more capacitive at frequencies below 20kHz because angular frequencies are inversely proportional to capacitive reactances.

This concludes our semester of circuit analysis lab assignments. It was such a fun semester solving circuit problems in lecture and reinforcing these concepts through experiments. I will definitely consider taking more electrical engineering courses in the future. I may consider taking a course in electronic devices in the near future.