Series Resonant Circuits

So far, we have merely considered AC circuits containing reactances of a single kind (capacitor or coil). Combining both these types of reactance results in an oscillating circuit. Due to their selective frequency properties they are usually called resonant circuits.

Oscillations are produced through periodic build-up and decay of an electric field (capacitance) or magnetic field (inductance). The following animation illustrates this.

The circuit diagram below shows a series resonant circuit consisting of a capacitor, inductor and an active resistance. The latter might also represent, for instance, the ohmic resistance of the coil .

Shown below is a vector diagram of voltages in this circuit. The voltages U_C and U_L across the capacitor and inductor are effectively in opposite directions.

For this reason, the total reactance of a series circuit is the difference between the inductive and capacitive reactance. The series circuit's apparent resistance is therefore as follows: