Define the quality factor (Q) of a resonant circuit.

Mathematically, the quality factor (Q) of a resonant circuit can be expressed as:

Q = 2π × (energy stored in the circuit) / (energy dissipated per cycle)

In practical terms, the quality factor relates to the sharpness of the resonance peak in the circuit's frequency response. A higher Q indicates a more defined and pronounced peak, whereas a lower Q results in a broader response curve. Resonant circuits with high-Q values are commonly used in applications where precise frequency selection and efficient energy storage are essential, such as in radio receivers, filters, and oscillators.

The quality factor is mathematically defined as the ratio of the energy stored in the circuit to the energy dissipated or lost in the circuit per cycle of oscillation. There are several ways to express the quality factor depending on the specific type of resonant circuit. For a series resonant circuit (consisting of an inductor and capacitor in series), the Q-factor can be expressed as:

Q = ω₀ * L / R

Where:

Q is the quality factor.

ω₀ (omega naught) is the resonant angular frequency of the circuit in radians per second.

L is the inductance of the coil in Henrys.

R is the resistance in the circuit in ohms.

For a parallel resonant circuit (consisting of an inductor and capacitor in parallel), the Q-factor can be expressed as:

Q = ω₀ * L / R

Where:

Q is the quality factor.

ω₀ (omega naught) is the resonant angular frequency of the circuit in radians per second.

L is the inductance of the coil in Henrys.

R is the resistance in the circuit in ohms.

In both cases, a higher Q-factor indicates that the circuit has lower losses and is more efficient at storing and transferring energy at its resonant frequency. High-Q resonant circuits are desirable in various applications where precise frequency selectivity and minimal energy loss are essential, such as in radio frequency (RF) communication systems, audio filters, and many other electronic devices.