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Two magnetically uncoupled inductive coils have $Q$ factors $q_{1}$ and $q_{2}$ at the chosen operating frequency. Their respective resistances are $R_{1}$ and $R_{2}.$ When connected in series, their effective $Q$ factor at the same operating frequency is 

  1. $q_{1} + q_{2}$
  2. $(1/q_{1}) + (1/q_{2})$
  3. $(q_{1}R_{1} + q_{2}R_{2})/(R_{1} + R_{2})$
  4. $(q_{1}R_{2} + q_{2}R_{1})/(R_{1} + R_{2})$
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