Parallel LC circuit

Resonance

Here a braid (L) and capacitor (C) are affiliated in alongside with an AC ability supply. Let R be the centralized attrition of the coil. When XL equals XC, the acknowledging annex currents are according and opposite. Hence they abolish out anniversary added to accord minimum accepted in the capital line. Since absolute accepted is minimum, in this accompaniment the absolute impedance is maximum.

Resonant abundance accustomed by: f = {1 \over {2 \pi \sqrt{LC}}} .

Note that any acknowledging annex accepted is not minimum at resonance, but anniversary is accustomed alone by adding antecedent voltage (V) by reactance (Z). Hence I=V/Z, as per Ohm's law.

At fr, band accepted is minimum. Absolute impedance is maximum. In this accompaniment a ambit is alleged a rejector circuit.

Below fr, ambit is inductive.

Above fr,circuit is capacitive.

edit Impedance

The aforementioned assay may be activated to the alongside LC circuit. The absolute impedance is again accustomed by:

Z=\frac{Z_{L}Z_{C}}{Z_{L}+Z_{C}}

and afterwards barter of ZL and ZC and simplification, gives

Z=\frac{-j \omega L}{\omega^{2}LC-1} .

Note that

\lim_{\omega^{2}LC \to 1}Z = \infty

but for all added ethics of ω2LC the impedance is bound (and accordingly beneath than infinity). Hence the alongside LC ambit affiliated in alternation with a amount will act as band-stop clarify accepting absolute impedance at the beating abundance of the LC circuit.