Two magnetically uncoupled inductive coils have Q factors q1 and q2 at the chosen operating frequency. Their respective resistances are R1 and R2. When connected in series, the effective Q factor of the series combination at the same operating frequency is

1
q1 + q2
2
(1/ q1) + (1/ q2)
3
(q1 R1 + q2 R2) / (R1 + R2)
4
(q1 R2 + q2 R1) / (R1 + R2)

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