02 March, 2007

Electrical Resonance and Resonant frequency

Electrical resonance occurs in an electric circuit at a particular resonant 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 a 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 wastage 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, ωL = 1/ωC, so:

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

Resonant freqency :
A resonant frequency is a natural frequency of vibration determined by the physical parameters of the vibrating object. This same basic idea of physically determined natural frequencies applies throughout physics in mechanics, electricity and magnetism, and even throughout the realm of modern physics.The lowest resonant frequency of a vibrating object is called its fundamental frequency. Some of the implications of resonant frequencies are:

1. It is easy to get an object to vibrate at its resonant frequencies, hard to get it to vibrate at other frequencies.
2. A vibrating object will pick out its resonant frequencies from a complex excitation and vibrate at those frequencies, essentially "filtering out" other frequencies present in the excitation.
3. Most vibrating objects have multiple resonant frequencies.

Resonant frequency is given by the expression :

For more details see the following links :http://en.wikipedia.org/wiki/Electrical_resonance

1 comment:

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