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, the effective $Q$ factor of the series combination at the same operating frequency is
- $q_1+q_2$
- $(1/q_1)+(1/q_2)$
- $(q_1R_1+q_2R_2)/(R_1+R_2)$
- $(q_1R_2+q_2R_1)/(R_1+R_2)$
