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
- $q_1R_1+q_2R_2$
- $q_1/R_1+q_2/R_2$
- $\big(q_1R_1+q_2R_2\big)/\big(R_1+R_2\big)$
- $q_1R_2+q_2R_2$