For improving the quality factor (Q) of a radio‐frequency coil (inductor), which choice of wire geometry is best: long, thin, thick, or long and thin? Explain considering Q = ωL / R and copper loss minimization.

Introduction / Context:
In electrical and electronics engineering, the quality factor Q of a coil indicates how efficiently it stores magnetic energy relative to resistive losses. A higher Q means lower copper loss and sharper resonance in tuned circuits. This question asks how the choice of wire affects Q when the inductance value is fixed by design.

Given Data / Assumptions:

• Quality factor: Q = ωL / R for a coil at angular frequency ω.
• Inductance L is set by turns, core/geometric form, and coil dimensions.
• Resistance R depends on wire length, cross-sectional area, temperature, and frequency (skin effect at RF).

Concept / Approach:
To increase Q at a given frequency and inductance, we must reduce the series resistance R. For a given resistivity ρ and length ℓ, R = ρℓ / A, where A is the conductor's cross-sectional area. A thicker wire increases A, which reduces R and thereby increases Q. A longer wire increases ℓ, which increases R and lowers Q. At radio frequencies, skin depth reduces the effective cross-section, further favoring thicker or Litz wire to keep R small.

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