RLC Circuit Demonstration
Dick Berg and Rich Baum, University of Maryland
We have constructed an RLC demonstrator circuit that actually allows you to simultaneously observe and compare the amplitudes and the relative phases of the four voltages in an RLC resonant circuit. This demonstration is classified as PIRA # 5L20.11 or some close permutation thereof, although existing descriptions do not seem to show the four traces simultaneously with four separate graphs due to grounding complications.
A standard variable-frequency sine-wave oscillator is tuned around the resonant frequency of about 20 kHz while the voltages across the source, the resistor, the capacitor, and the inductor are viewed simultaneously on a four-trace (or two dual-trace) scope(s). The four signals - from the source, R, L, and C - are isolated from ground using linear isolation transformers with impedance much greater than that of the circuit elements, so that it observes the circuit without affecting it. Phases are rendered independent of any of the four signals being observed by triggering the oscilloscope on the trigger output from the signal generator. By switching out either the capacitor or the inductor measurements can be made for an RL or RC circuit, respectively.
The figure is a photograph of the entire demonstration. A four-trace Tektronix TDS series digital oscilloscope is positioned on an old Tektronix scopemobile with a plywood platform mounted on its top. On the platform are a Wavetek signal generator and the box containing the RLC circuit with the isolation transformers. The effective RLC circuit is drawn on the front of the box, indicating the positions of the R, L, and C, but not the isolation transformers. The wave generator input BNC connector is labeled, while the connectors across each of the four circuit elements (source, R, L, C) on the outside of the circuit allow observation of the voltage across each of these elements. The system is triggered by an external trigger input on the back of the oscilloscope and set to trigger at the center of the screen, so that the part of the wave at the center of the oscilloscope remains at the same phase at all times.
The TDS series of oscilloscopes outputs an EGA compatible video signal that is displayed using a computer monitor on the scopemobile platform, as seen at the top in the photograph. The monitor allows the oscilloscope screen to be visible throughout small classrooms, while in larger lecture halls the output is converted to RGB and sent to a ten-foot diagonal in-house video projector.
In a series circuit such as this the current in all of the elements must be the same amplitude and in the same phase. Thus what you are actually seeing and comparing are the voltages across the input, R, L and C.
You can readily observe:
1. The input signal remains constant in phase and very nearly constant in amplitude as the frequency is swept.
2. The voltage across the resistor is maximized at the resonant frequency.
3. The voltage across the resistor is in phase with the input voltage at resonance.
4. The voltage across the capacitor lags the current by 90o at all frequencies.
5. The voltage across the inductor leads the current by 90o at all frequencies.
6. The voltages across the capacitor and the inductor are equal and opposite at the resonant frequency.
7. As the frequency is swept through resonance, the peak of the voltage across the resistor leads that of the applied voltage below the resonant frequency and lags the applied voltage above the resonant frequency.
8. The increase in capacitive reactance as the frequency becomes lower causes greater voltage across the capacitor, and drives the phase of the voltage across the resistor to lead the applied voltage.
9. The increase in inductive reactance as the frequency becomes higher causes greater voltage across the inductor, and drives the phase of the voltage across the resistor to lag the applied voltage.
The complete electrical circuit can be downloaded from the URL We used a 0.1 microfarad capacitor, a 1 millihenry, 6 Ohm inductor, and a 0-500 Ohm variable resistance that we set to about 100 Ohms for the basic resonance demonstration. This gives a calculated resonant frequency of about 16 kHz. The reactances of the inductor and the capacitor are about 100 Ohms near that frequency. Because the pure resistance of the inductor is only 6 Ohms, much smaller than its inductive reactance near resonance, it acts very nearly like a pure inductance in the RLC circuit. The linear isolation transformers used are MagneTek #SP-70, with 600 Ohms impedance over the frequency range 50 Hz to 100 kHz. Near the resonance this means that their impedance is somewhat greater than that of the components used in the RLC circuit itself, so they do not have a significant effect on the properties of the basic RLC circuit. Note that the actual resonant frequency is a bit higher than the theoretical frequency calculated using the capacitance and inductance above, but this affects the experiment very little.
A large number of more basic demonstrations can be carried out using this setup. By switching out the inductor an RC circuit is obtained, and by switching out the capacitor an RL circuit is obtained. In both cases the phases of voltages across the circuit elements can be observed and compared with theory for a variable-frequency AC source. Using a low-frequency square wave, ringing is created when the wave changes polarity. The damping of the circuit can be changed by varying the resistance.