Editing LC circuit (section)

=== Resonance ===
When {{mvar|X}}{{sub|L}} equals {{mvar|X}}{{sub|C}}, the two branch currents are equal and opposite. They cancel each other out to give minimal current in the main line (in principle, for a finite voltage {{mvar|V}}, there is zero current). Since total current in the main line is minimal, in this state the total impedance is maximal. There is also a larger current circulating in the loop formed by the capacitor and inductor. For a finite voltage {{mvar|V}}, this circulating current is finite, with value given by the respective voltage-current relationships of the capacitor and inductor. However, for a finite total current {{mvar|I}} in the main line, in principle, the circulating current would be infinite. In reality, the circulating current in this case is limited by resistance in the circuit, particularly resistance in the inductor windings.

The resonant frequency is given by
: <math>f_0 = \frac{ \omega_0 }{\ 2 \pi\ } = \frac{1}{\ 2 \pi \sqrt{ L C\;}\ } ~.</math>

Any branch current is not minimal at resonance, but each is given separately by dividing source voltage ({{mvar|V}}) by reactance ({{mvar|Z}}). Hence  {{math|''I'' {{=}} ''{{sfrac| V |Z}}''}} , as per [[Ohm's law]].

* At  {{math|''f''<sub>0</sub>}} , the line current is minimal. The total impedance is maximal. In this state a circuit is called a ''rejector circuit''.<ref>{{cite web |url=https://en.oxforddictionaries.com/definition/rejector_circuit |archive-url=https://web.archive.org/web/20180920195850/https://en.oxforddictionaries.com/definition/rejector_circuit |url-status=dead |archive-date=September 20, 2018 |title=rejector circuit |website=Oxford Dictionaries. English |access-date=2018-09-20}}</ref>
* Below  {{math|''f''<sub>0</sub>}} , the circuit is inductive.
* Above  {{math|''f''<sub>0</sub>}} , the circuit is capacitive.