In electricity, the behavior of an alternating circuit (AC) is determined by whether its circuit elements are connected in series or in parallel. Resonance describes a characteristic frequency determined by the values of the resistance (in units of ohms), capacitance (in units of farads), and inductance (in units of henrys) of the circuit. There are accordingly two types of resonance: series resonance, for which the condition of resonance is minimum impedance and zero phase, and parallel resonance, the most common in electronic applications, for which the condition of resonance is minimum current and a phase change.
A circuit consisting of resistors, inductors, and capacitors connected in series obeys Kirchhoff's voltage law which states that the sum of the emf's in a closed circuit is equal to the sum of the potential difference of the components. The reactance of the circuit is equal to: X = L - 1/C where is the circuit frequency, L is the inductance and C the capacitance. The reactance is dependent on the frequency of the voltage ƒ = /(2). The impedance (Z) of such a circuit is:
where R is the resistance. The phase angle is: PH = arctan {[L-1/(C)]/R} and resonance occurs in the circuit when the capacitive and inductive reactance increases. The total resistance is then equal to the ohmic resistance R and the current flow is at a maximum. The resonant frequency is given by:
At the resonant frequency, current and driving voltage are in phase because the phase angle is zero, the impedance Z is at a minimum, and the power dissipated is at a maximum.
A circuit consisting of resistors, inductors and capacitors connected in parallel obeys Kirchhoff's current law which states that the sum of the currents flowing into a junction is equal to the sum of the currents flowing out. In this case, the reactance of the circuit is equal to: X = C - 1/L and it is also dependent on the frequency of the voltage ƒ = /(2). The impedance (Y) of the circuit is:
The phase angle is given by: PH = arctan [RC-R/(L)]. Resonance occurs when the circuit frequency is such that the inductive and capacitive reactances are fully compensated. The resonant frequency is also equal to:
At the resonant frequency of a parallel circuit, the current is at a minimum and the phase angle changes by 180°.
AC circuit resonance is the operating principle for building devices designed to process signals of a given frequency while rejecting others. In a television receiver, for example, resonance occurs when the frequency of one of the incoming signals reaching the circuit is close to the circuit frequency, which can then absorb maximum energy from the signal as the current flowing through the circuit surges back and forth in step with the current flowing in the antenna. Another example of electric resonance occurs when tuning a receiver to listen to a broadcast. Tuning modifies the setting of the tuning capacitor of the radio. When the radio circuit reaches a frequency resonant with that of the broadcast frequency, the induced voltage is increased and processed into sound.
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