Performance-Based Assessments for AC Circuit Competencies

Use a sine-wave function generator for the AC voltage source. Specify a cutoff frequency within the audio range.

I recommend setting the function generator output for 1 volt, to make it easier for students to measure the point of “cutoff”. You may set it at some other value, though, if you so choose (or let students set the value themselves when they test the circuit!).

I also recommend having students use an oscilloscope to measure AC voltage in a circuit such as this, because some digital multimeters have difficulty accurately measuring AC voltage much beyond line frequency range. I find it particularly helpful to set the oscilloscope to the “X-Y” mode so that it draws a thin line on the screen rather than sweeps across the screen to show an actual waveform. This makes it easier to measure peak-to-peak voltage.

The real challenge in this assessment is for students to determine their transformers’ “polarities” before connecting them to the AC voltage source! For this, they should have access to a small battery and a DC voltmeter (at their desks).

You may use a Variac at the test bench to provide variable-voltage AC power for the students’ transformer circuits. I recommend specifying load resistance values low enough that the load current completely “swamps” the transformer’s magnetization current. This may mean using wire-wound power resistors instead of 1/4 watt carbon composition resistors.

Note that there may very well be a shock hazard associated with this circuit! Be sure to take this into consideration when specifying load resistor values. You may also want to use low supply voltage levels (turn the Variac way down).

An extension of this exercise is to incorporate troubleshooting questions. Whether using this exercise as a performance assessment or simply as a concept-building lab, you might want to follow up your students’ results by asking them to predict the consequences of certain circuit faults.

This is perhaps the most reliable means of measuring inductance without an impedance bridge or an LCR meter. You may wish to ask your students to explain why this method of measurement is so good (hint: they must explain why the inductor’s intrinsic resistance has no effect on the measurement).

I prefer this particular circuit design for L measurement because series resistance does not skew the resonant point, and because the series capacitor prevents any possible DC current from “biasing” the inductor’s core.

If your students own high-quality multimeters capable of measuring audio-frequency AC current and frequency, then the best way to do this is to replace the resistor R₁ with their ammeters. Otherwise, use an oscilloscope to measure (maximum) voltage dropped across R₁.

In order to obtain good measurements using this technique, I recommend following these guidelines:

Choose a value of R₁ low enough to give a sharp bandwidth, but not so low that the voltage signal dropped across it is “fuzzy” with noise and difficult to accurately discern the period of.

Choose a value for C₁ as low as possible to give sharp bandwidth (thereby maximizing the ^L/_C ratio), without pushing the circuit’s resonant frequency too close to the inductor’s self-resonant frequency.

Avoid frequencies above the audio range, lest your students measure the inductor’s self-resonant point!

Use minimal output from the signal generator, to avoid voltage and current levels that will approach core saturation in the inductor.

I’ve had fair results using one of the windings of a small audio output transformer (center-tapped 1000 Ω primary winding, with 8 Ω secondary winding) as the inductor, connected in series with either a 0.1 μF or a 0.47 μF metal-film capacitor, all in series with a 100 ohm resistor. For best results, of course, pre-measure the value of the capacitor rather than go by its advertised value.

I have also used a 100 mH inductor (nominal), in series with a 0.033 μF capacitor and 100 Ω resistor, with good results.