Caltech LRC Laboratory

Welcome to the LRC Circuit Lab

This Java applet is intended to show you how a system of a resistor, a capacitor and an inductor react with one another in a system.

There are a couple of important limitations of this system

  • You can't reorganise the components, or apply the input at different places

  • You can't observe voltages other than those coded in the demo

  • Components set to zero are still shown

Notes

  • Blue is used for voltage
  • Red is used for current
  • Stop - shows amplitude and phase
  • Run - shows rotating phasors illustrating the exp(jwt) dependence
  • Step - increments the time by a small step

Outline instructions to illustrate key ideas

  • Set L to 0 (to exclude the inductor)
  • Set C to 0 (to exclude the capacitor)
  • Set R to 5 ohms

Note: the graphic display still shows the L and C despite the fact that both have been 'excluded'.  You need to think of them as short-circuits in this illustration

  • Vary the voltage using the slider
  • Press Start - NB anticlockwise rotating phasor sketches out a sinusoidal waveform

Note that the time axis is not 'real' time - it is 100 times slower.

Inductive reactance

  • Vary the frequency and voltage using the sliders and observe the effect: also, note that current and generator voltage are in phase.  Vary the resistance and note that while the current varies, the phase does not change
  • Press Stop, then Step, repeatedly, until the Blue & Red arrows lie at 0 (horizontal, pointing to R)
  • Set the frequency to 50 rad/s (about 8 Hz); set voltage to 25 rms; set R to 5 ohms
  • Add some inductance, gradually, up to about 60 mH. 

Note how the red current phasor begins to lag behind the a/c/w-rotating voltage phasor.  Observe that the CIVIL mnemonic correctly predicts this.

  • Vary L - a higher value increases the phase lag
  • Vary f to show how the phase and amplitude of the current are affected

Capacitive reactance

  • Reduce L to 0 (NB the blue/red phasors now coincide)
  • Set f to 100 rad/s
  • Set C to 5 mF

Note that the red phasor now leads the blue voltage phasor

  • Change C and note that an increase reduces the phase lead
  • Change f and note that increasing it reduces the phase lead

Resonance

  • Set the capacitance to 8 mF, f to 50 rad/s - I will lead V by about 30 deg.
  • Now set R to 2, V to 14 rms
  • Slide the L slider down and note how increasing L reduces the phase lead seen. 

At a certain value of L, the current neither leads nor lags.  The inductive and capacitive reactance have cancelled.  This happens at one characteristic frequency: the resonant frequency.