The resonant frequency is the natural frequency at which an object or system tends to vibrate with the greatest amplitude when energy is supplied at that frequency. In a physical system, this frequency depends on the system's shape, mass, and elasticity. For example, a swing or a musical instrument vibrates strongly at its resonant frequency when pushed or played at that specific frequency. In electrical circuits, especially those involving inductors and capacitors (LC circuits), the resonant frequency is the frequency at which the inductive reactance equals the capacitive reactance, resulting in efficient energy transfer and maximum voltage or current. The formula for the resonant frequency f0f_0f0 in an LC circuit is:
f0=12πLCf_0=\frac{1}{2\pi \sqrt{LC}}f0=2πLC1
where LLL is the inductance and CCC is the capacitance. At this frequency, circuits can show either a minimum or maximum impedance depending on the configuration (series or parallel), leading to different electrical behaviors such as maximum current in a series RLC circuit or maximum impedance in a parallel one. The concept of resonant frequency applies broadly in physics, engineering, and audio technology, influencing the design and function of mechanical systems, electronic circuits, and acoustic devices.
