Electrical resonance

Electrical resonance occurs in an electric circuit at a particular "resonance frequency" when the impedance between the input and output of the circuit is at a minimum (or when the transfer function is at a maximum). Often this happens when the impedance between the input and output of the circuit is zero and when the transfer function equals one.

Resonance with capacitors and inductors

Resonance of a circuit involving capacitors and inductors occurs because the collapsing magnetic field of the inductor generates an electric current in its windings that charges the capacitor, and then the discharging capacitor provides an electric current that builds the magnetic field in the inductor, and the process is repeated continually. An analogy is a mechanical pendulum. In some cases, resonance occurs when the inductive reactance and the capacitive reactance of the circuit are of equal magnitude, causing electrical energy to oscillate between the magnetic field of the inductor and the electric field of the capacitor.

At resonance, the series impedance of the two elements is at a minimum and the parallel impedance is at maximum. Resonance is used for tuning and filtering, because it occurs at a particular frequency for given values of inductance and capacitance. It can be detrimental to the operation of communications circuits by causing unwanted sustained and transient oscillations that may cause noise, signal distortion, and damage to circuit elements.

Parallel resonant or near-to-resonance circuits can be used to prevent the waste of electrical energy, which would otherwise occur while the inductor built its field or the capacitor charged and discharged. As an example, asynchronous motors waste inductive current while synchronous ones waste capacitive current. The use of the two types in parallel makes the inductor feed the capacitor, and "vice versa", maintaining the same resonant current in the circuit, and converting all the current into useful work.

Since the inductive reactance and the capacitive reactance are of equal magnitude, ω"L" = 1/ω"C", so:

:$omega\; =\; frac\{1\}\{sqrt\{LC$

where ω = 2π"f", in which "f" is the resonance frequency in hertz, "L" is the inductance in henries, and "C" is the capacitance in farads when standard SI units are used.

See also

* Antenna theory
* Cavity resonator
* Resonance
* RLC circuit
* Electronic filter

References