Caltech LRC Laboratory
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
You can't observe voltages other than those coded in the
Components set to zero are still shown
- Blue is used for voltage
- Red is used for current
- Stop - shows amplitude and phase
- Run - shows rotating phasors illustrating the exp(jwt)
- 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
- Vary the voltage using the slider
- Press Start - NB anticlockwise rotating phasor sketches out a sinusoidal
Note that the time axis is not 'real' time - it is 100 times slower.
- 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
- 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
- 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
- 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
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.