The frequency at which resonance in a tuned LC circuit occurs is given by the following formula: fr = 1 / [2π(sqrt(LC))] where fr = resonant frequency (Hz); L = the inductance (H); and C = the capacitance (F).
Using the above equation, one can calculate either the value of the inductance L or capacitance C that will result in resonance at a given frequency fr: L = 1 / [4π2fr2C] or C = 1 / [4π2fr2L].
The reactance of an inductance L is equal to 2πfL while that of a capacitance C is equal to 1/2πfC.
Thus, for a series RL circuit, the quality factor Q is given by the equation: Q = 2πfrL / R. On the other hand, the quality factor Q for a series RC circuit is given by the equation: Q = 1 / 2πfrCR.
Since Q is the ratio of the resonant or center frequency fr to the bandwidth B, Q is a measure of the 'sharpness' of the response of the tuned circuit to the resonant frequency.
Thus, a circuit with a high Q will exhibit a higher amplitude at the resonant frequency, but will decay more quickly as the frequency moves away from the resonant frequency.
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The term "resonance" literally translates as "to vibrate with".
In physics, resonance is the phenomenon wherein two systems are vibrating within the same frequency range, creating order.
In electronics, resonance is a state wherein a tuned circuit's capacitive reactance is equal to its inductive reactance.
A series LC circuit that is in resonance, i.e., excited by a signal at its resonant frequency, exhibits zero reactance.
On the other hand, a parallel LC circuit exhibits infinite reactance at its resonant frequency.
Series and parallel LC circuits may therefore be combined to form either a band-pass filter or a band-stop filter.
The frequency at which resonance in a tuned LC circuit occurs is given by the following formula:
fr = 1 / [2π(sqrt(LC))] where
fr = resonant frequency (Hz);
L = the inductance (H); and
C = the capacitance (F).
Using the above equation, one can calculate either the value of the inductance L or capacitance C that will result in resonance at a given frequency fr: L = 1 / [4π2fr2C] or C = 1 / [4π2fr2L].
The ratio of the reactance of the tuned circuit to its resistance is called the "quality factor", or Q factor, or simply Q.
Thus, Q is the ratio of the energy stored to the energy dissipated in the circuit per cycle.
The reactance of an inductance L is equal to 2πfL while that of a capacitance C is equal to 1/2πfC.
Thus, for a series RL circuit, the quality factor Q is given by the equation: Q = 2πfrL / R. On the other hand, the quality factor Q for a series RC circuit is given by the equation: Q = 1 / 2πfrCR.
The quality factor Q of a tuned circuit is given by the equation:
Q = fr / B
where B is the bandwidth of the circuit in Hz.
The bandwidth of a circuit is the frequency interval between its half-power points f2 and f1, or B = f2 - f1. Thus,
Q = fr / (f2 - f1).
Since Q is the ratio of the resonant or center frequency fr to the bandwidth B, Q is a measure of the 'sharpness' of the response of the tuned circuit to the resonant frequency.
Thus, a circuit with a high Q will exhibit a higher amplitude at the resonant frequency, but will decay more quickly as the frequency moves away from the resonant frequency.
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