Impedance of series RLC circuits

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Background

This applet illustrates the physics of resonance in series RLC circuits in an interactive manner. The physical setup is a series circuits made up of a capacitor of capacitance C, an inductor of inductance L, a resistor of resistance R, and a source of alternating voltage. The circuit is shown below:

The frequency of the alternating voltage and current is f. The corresponding angular velocity is ω = 2πf. Voltage and current are sinusoidal functions of time and are represented graphically by the horizontal component of a rotating arrow called a phasor. In practice, phasors are drawn as fixed arrows, corresponding to a snapshot of the rotating phasor at some arbitrary point in time. The advantage of the phasor representation is that it gives a graphical representation of the relative phases and magnitudes of various sinusoidal functions.
It can be shown that:

By application of Kichhoff's current law, the current is the same throughout the circuit.
By application of Kichhoff's voltage law, the voltage across the source is equal to the sum of the individual voltages. The phasor for the voltage across the source is represented by the vector sum of the phasors for the individual voltages across the resistor, the capacitor, and the inductor.

The ratio of the r.m.s values of voltage and current for the whole circuit is Z, the impedance of the circuit. One can think of resistance as the part of impedance that does dissipate energy and one can think of reactance as the part of impedance that does not dissipate energy. Impedance is a measure of the ratio of the r.m.s value or voltage required to have a unit r.m.s value of current.
A simple application of the Pythagorian theorem gives:

Resonance happens at a frequency of:

At that frequency, we have the following:

Using the applet

All the controls are located at the bottom of the applet. The controls include four sliders and a series of three radio buttons. The sliders allow the user to set the values of R, C, L and f. The voltage amplitude is equal to 1 volt. The radio buttons allow the user to choose which graph the applet will display. The user can choose one of the following four graphs:

In addition to these graphs, the applet displays the phasor diagram for the circuit.