Step 1: Understanding the Concept:
In an LCR (Inductor, Capacitor, Resistor) series circuit, resonance occurs at a specific frequency where the inductive reactance cancels the capacitive reactance, allowing maximum current to flow.
Step 2: Key Formula or Approach:
The Quality Factor ($Q$) is a dimensionless parameter formally defined as the ratio of the resonant frequency $f_0$ to the bandwidth $\Delta f$:
\[ Q = \frac{f_0}{\Delta f} = \frac{\omega_0 L}{R} \]
where $\Delta f = f_2 - f_1$ is the difference between the half-power frequencies.
Step 3: Detailed Explanation:
The bandwidth $\Delta f$ defines the range of frequencies around the resonant frequency where the power dissipated is at least half of its maximum peak value.
A large $Q$-factor means that the bandwidth $\Delta f$ is very small.
Graphically, plotting current versus frequency for a circuit with a small bandwidth yields a very narrow, tall, and highly pointed peak.
Conversely, a low $Q$-factor results in a wide bandwidth, giving a flat and broad peak.
Because a high $Q$-factor creates a sharper peak, it allows the circuit to be highly selective in tuning to one specific frequency while rejecting others (like tuning a radio).
Therefore, the physical significance of the $Q$-factor is that it measures the sharpness of resonance.
Step 4: Final Answer:
The correct option is (B).