LC circuit

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An LC circuit is an electronic circuit made up of an inductor and a capacitor.

LC circuit's resonant frequency is equal to:

The angular frequency ω has units of radians per second.

LC circuits are used for creating signals at a particular frequency, or picking out a signal at a particular frequency from a more complex signal. An ideal LC circuit does not have resistance.

At LC circuit energy saves in the capacitor's electric field.

U is energy and q is electric charge. At LC circuit energy also save in the inductor's magnetic field.

U is energy and i is electric current that flows in inductor.

Let's analyze an LC circuit's vibration. Vibrating LC circuit's total energy is U.

Because circuit's resistance is 0, there is no energy that transmits to heat energy, and U is maintained regularity.

So LC circuit's vibration is shown like that

First consider the Electrical impedance of the series LC circuit. The total impedance is given by the sum of the inductive and capacitive impedances

By writing the inductive impedance as and capacitive impedance as


Resultingly the series connected circuit, when connected to a circuit in series, will act as a band-pass filter having zero impedance at the resonant frequency of the LC circuits.


and after substitution of and we have

which simplifies to


Resultingly the parallel connected circuit will act as band-stop filter having infinite impedance at the resonant frequency of the LC circuit.

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