Inductor quality factor (Q): For a practical inductor modeled as an ideal L in series with winding resistance R, the quality factor Q at a given frequency is the ratio of inductive reactance to resistance, Q = X_L / R. Decide whether this statement is correct.

Introduction / Context:Quality factor quantifies how reactive energy storage compares to resistive loss. For inductors using the common series R-L model, Q is a simple and widely used measure in filters, resonant tanks, and RF chokes.

Given Data / Assumptions:

• Series model: L with series R (winding and equivalent losses).
• Operating at a single frequency f (since X_L depends on f).
• Inductive reactance X_L = 2 * pi * f * L.

Concept / Approach:Define Q for a series inductor as Q = X_L / R. Larger Q means lower loss relative to reactance. At resonance in an RLC, higher Q leads to narrower bandwidth. This definition is frequency-dependent and is appropriate when resistance is small compared to reactance (high-Q devices).

Step-by-Step Solution:

Verification / Alternative check:Compare two inductors at the same f and L but different R; the one with lower R has higher Q, behaving closer to an ideal inductor (sharper resonance, lower insertion loss).

Why Other Options Are Wrong:

• Incorrect/DC only: At DC, X_L = 0, so Q is undefined/zero. The relation applies at AC.
• Core material only: Core affects losses and L, but Q still uses X_L/R.

Common Pitfalls:Confusing series and parallel Q definitions; forgetting frequency dependence; ignoring additional core-loss components that can be folded into an effective R for small-signal models.

Final Answer:Correct