In the context of A.C. (alternating current) fundamentals, "sharpness of resonance" refers to the degree to which a resonant circuit or system can amplify a specific frequency of alternating current. Resonance occurs when the reactive components (inductors and capacitors) in a circuit balance each other out, resulting in a maximum response at a particular frequency.
The sharpness of resonance is determined by the quality factor (Q-factor) of the resonant circuit. The Q-factor is a dimensionless parameter that indicates how "selective" the circuit is in amplifying a narrow range of frequencies around the resonant frequency. A high Q-factor indicates a sharp resonance, meaning the circuit responds strongly to a very specific frequency and has a narrow bandwidth.
Mathematically, the Q-factor can be calculated using the following formula:
Q = fâ / Îf
where:
Q is the quality factor
fâ is the resonant frequency
Îf is the bandwidth of the circuit (the range of frequencies around the resonant frequency where the response is significant)
A circuit with a high Q-factor will have a steep response curve centered around the resonant frequency, resulting in a sharp peak in the amplitude of the current or voltage. In contrast, a circuit with a low Q-factor will have a broader response curve and a less pronounced peak.
Applications of circuits with sharp resonance include radio tuning circuits, filter circuits, and impedance matching networks. These circuits are designed to respond strongly to a specific frequency while rejecting or attenuating other frequencies. The sharpness of resonance allows for precise frequency selection and filtering in various electronic systems.