Inductive Reactance


Inductive Reactance, $X_{L_{p}}$

If we expand $X_{L_{p}}$ as, which was derived in the topic (Parallel Resonant Circuit)
$$\begin{split} X_{L_{p}} &= { R^2_l + X^2_L \over X_L }\\ & = { R^2_l (X_L) \over X_L(X_L) } + X_L\\ &={ X_L \over Q^2_L } + X_L\\ \end{split}$$
then, for $Q_l \geq 10$, $X_L/Q_l^2 \approx 0$ compared to $X_L$ , and
$$X_{L_{p}} \approx X_L $$
and since resonance is defined by $X_{L_{p}} = X_C$, the resulting condition for resonance is reduced to:
$$ X_L \approx X_C \,\, \text{ (Ql>10)}$$

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