We have been analyzing AC circuits for a few weeks now. The reality of how the circuit behaves will feel a little different than the mathematical representation for most students. There is also just a lot of stuff that we need to learn how to use in order to make even simple measurements of AC circuits. This lab is intended to be a first experience with using the function generator and the digital oscilloscope to make specific measurements and plot them.
I will be watching to see how the lab is developing. If it seems like we need more time to explore this experimental setting more completely or better understand the equipment we will extend this lab through next week. There is a lot to do here and I dont' want you to be rushed as you develop your understanding.
Purpose:
To explore the relationship between what we calculate/analyze in an academic setting and what that looks like in the wild where the resistors and capacitros are not some industrialized or sanitized objects but rather free range devices with a mind of their own.
We will wire the following circuit with the illustrated components on a simple protoboard (which you learned all about in ENGR 201, right?). The capacitor may have various values which is why it isn't stated at this point. I want to note that the reason for having two resistors in the circuit is to assure that even if there are missteps in the lab the function generator will (hopefully) be protected from damage. Before you start wiring anything up I want you to solve this circuit (in your notebook) for any angular frequency (what frequency does the function generator display?) so that you can describe the voltage drop, amplitude and phase, across either resistor. You should find that both the amplitude and the phase depend on the angular frequency. Determine the angular frequency at which the impedance of the capacitor is equal to that of the total series resistance.
Several things to note about the set up. It is very handy to be able to see the voltage source on one of the oscilloscope channels as a constant reference. This allows you to monitor the amplitude, phase, and frequency. To do this you can attached the BNC T connector to the function generator and run one BNC cable to the scope and one to the circuit. Given the physical set up of our digital scopes it might make sense to use channel 2 for this to keep the cables out of the way. Select the frequency for the function generator that you determined makes the impedance of the capacitor equal to that of the resistors.
At this point you can verify that your AC source has the appropriate amplitude and DC offset (no offset in today's lab) BEFORE you connect it to your circuit. Note: If you have connected the function generator to channel 2 on the scope you will need to select CH2 as your trigger source on hte scope control panel. The BNC to clip connector allows you to easily connect the second output of the T to your circuit as indicated. The red clip lead is (+) by convention and the black is (-). You may find that when you attach the function generator to the circuit that it seems to change. If this is significant (it wasn't for me) then the implication is that your circuit is overstressing the internal electronics of the function generator. Stop and check everything and get input from your lab instructor before proceeding if this happens.
Now you can select another BNC cable with a BNC to clip lead adaptor on one end that you can use as a tool to probe the circuit. This cable is attached to the unused channel of your scope at one end and the clip leads connect to the object (the second resistor in our case) that we are seeking to measure. Be sure that the ground lead (the black clip) is connected to the same end of the resistor to avoid confusing ground loops. Again, if your scope trace of the voltage from the function generator changes significantly stop and seek input from your lab instructor. Otherwise you should now be able to "see" the trace of the AC voltage across the resistor on the other channel of your scope.
At this point you can determine the amplitude of the voltage signal across the resistor and it's phase shift relative to the source voltage generated by the function generator. Do so and be sure you understand how this relates to the initial calculations that you made for this lab.
Now, the bigger picture. Explore the full range of frequencies available to you on the function generator and determine the amplitude and phase shift of the voltage across the resistor. This will cover several orders of magnitude so you should plan how to collect your data for a semi log plot. You will find that there is a particular range where the phase and amplitude change more rapidly and the wise student will take added data points in this range. In particular be sure to determine the frequency at which the phase shift is 45 degrees. Record all this data in your notebook (goes without saying:).
Similar analyses apply to inductive (L) circuits.
Deliverables:
I) The usual date, description of equipment, lab partners, etc etc for openers.
II) Your quick, yet complete, analysis of the circuit and your description of what you expect to observe when you measure the voltage and phase across the resistor.
III) The data you collected for the amplitude and phase of the voltage across the resistor for the full range of frequencies.
IV) A semi-log plot of the data from III. Put both sets of data on the same plot with different symbols. Discuss your observations about this plot and what you might glean from similar plots.
Thanks in advance for the gorgeous plots!!
