# 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

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.