Electrical Resonance

Resonance

What's Resonance?

resonance is the state at which any element is naturally oscillate at the frequency they like to oscillate 

when connecting an initially charged capacitor with an inductor we notice that energy which stored at capacitor as an electric field transfer to inductor which store energy as magnetic field.

so what happen there?
capacitor charge indutor until it fully charged so capacitor at this moment fully discharged then inductor charge capacitor back until it fully charged and indutor fully discharged. this cycle continues forever if there's no losses in the wiring system but in fact this energy gradually die out because of losses.
this circuit act like a pendulum, in pendulum kinetic energy transfer into potential energy then potential transfer into kinetic and so on until it stops because of losses so LC circuit and pendulum oscillate at frequency they like
 so this state is called resonance.

Condition Of Electrical Resonance Occurrence:

Resonance in electrical system occur when supply drives circuit at resonance frequency.
at resonance frequency capacitor reactance is equal inductor reactance.

So resonance  frequency is:

Series Combination Of RLC Circuit In Resonance:

when applying voltage source with frequency equal to resonance frequency the combination of LC will act like a short circuit. 
as circuit element are connected in series so the current is the same passing through all element RLC so let us consider the current as reference.

at inductor: 
the voltage leads the reference current by 90 degree.
at capacitor:
the voltage lags the reference current by 90 degree.

so when adding capacitor voltage and inductor voltage at resonance we notice that they have the same magnitude and out of phase by 180 degree and the resultant voltage become zero so that LC acting like short circuit and the series resistor have all supply voltage.




Parallel Combination Of RLC Circuit In Resonance:

when connecting element in parallel the voltage is the same at the capacitor and inductor so let us take it as a reference.
 
at inducor: 
the current lags the reference voltage by 90 degree.
at capacitor:
the current leads the reference voltage by 90 degree.

so when adding capacitor current and indutor current together at resonance we notice that they have the same magnitude and out of phase by 180 degree so the resultant current become zero and combination of LC act like an open circuit and all current is passing through the resistor only.