Ideas in Teaching AC

Denis Burchill

The Series LCR Circuit at Resonance.

A significant number of teachers find practical experiments or demonstrations in AC resonance difficult to do. A first requirement is the right equipment. The most useful pieces of equipment are a dual trace oscilloscope (CRO), a Unilab signal generator or equivalent (with a capacity to deliver 1 ampere) and a digital multimeter preferably with frequency and capacitance measurement functions.

Major problems:

1. Many inductors have significant series resistance. This makes it harder to identify the phases between the various voltages: Vgen, VC, VL and VR and consequently more complex to draw the resulting phasor diagram. A computer spreadsheet simulation can be used to assist in both simple and complicated situations. (Contact the author to obtain a copy of an AC resonance spreadsheet in Excel format.) 
2. Both the CRO and the signal generator are "grounded", i.e. they are both connected to the "earth" wire in the mains supply. This limits the range of phase relationships between the voltages in the LCR circuit that you can display on the CRO.

For example:

In this arrangement the Vgen/VR phase relationship can be displayed. Alternatively L & R can be swapped to display Vgen/VL and similarly C & R can be swapped to display Vgen/VC. But you cannot show VR/VC, VR/VL, VC/VL at all easily since the ground on the signal generator is always connected to the ground on the CRO.

Solutions:

1. Connect a battery powered "buffer" amplifier to the output of the signal generator. This provides a voltage output (Vgen) that is not connected to the ground. A voltage output like this is called a "floating" voltage.
   
   
2. Use an isolating transformer to power either the CRO or signal generator and so make one of the devices "float". This has worked successfully.
   
   
3. Make up a double circuit of identical components as shown in the following circuit diagram.

The phase between VR and VL can be displayed using the arrangement above. Component values that work well are: R = 100 ohm, C = 1.0 microfarad, L = 0.0041 henry approximately (i.e. the common PSSC solenoid). This gives a resonant frequency of about 3 000 Hz.

Components can be interchanged so that all the voltage combinations can be displayed in this arrangement. Also, the connections to the CRO will be the "right way round" so that you do not have to push the "invert" button on one of the CRO inputs as you would have to using solutions 1 & 2.

Other Hints:

1. Replace the resistor with a light bulb. The light bulb will only glow when the signal generator's frequency is near resonance.
   
   
   
   
2. Where possible keep the series resistance low so that the resonance is "sharp" and well defined. However if the resistance is too low then too much current will flow at resonance and will "load" the signal generator causing the voltage of Vgen to dip at resonance.