Step 1: Understanding the Concept:
The Quality Factor (\(Q\)-factor) is a dimensionless parameter that describes how under-damped an oscillator or resonator is.
In the context of electrical tuned circuits (like an LCR circuit), it characterizes the sharpness of the resonance peak.
Step 2: Key Formula or Approach:
Mathematically, the \(Q\)-factor is defined as the ratio of the resonant frequency to the bandwidth (the difference between the upper and lower half-power frequencies).
\[ Q = \frac{\text{Resonant Frequency}}{\text{Bandwidth}} \]
Step 3: Detailed Explanation:
Using standard notation, if \(f_0\) is the resonant frequency and \(\Delta f = f_2 - f_1\) is the bandwidth:
\[ Q = \frac{f_0}{f_2 - f_1} = \frac{f_0}{\text{Bandwidth}} \]
A higher \(Q\) value indicates a narrower bandwidth relative to the resonant frequency, meaning the circuit is highly selective. Conversely, a lower \(Q\) value corresponds to a wider, flatter resonance curve.
Step 4: Final Answer:
The correct mathematical definition given the options is \(Q = \frac{f_0}{\text{Bandwidth}}\).