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# RLC resonance

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#### smtareq

##### New Member
Hello everyone,
I'm a total newbie in electronics. I've studied RLC series and parallel resonance theory and learned that energy is pulsed back and forth between capacitor and inductor during resonance and the reactances for L & C must be equal. But my question is "Why resonance occurs when the reactances are matched?"
I'v googled and found that when something is made to oscillate at its "natural" frequency then resonance will occur. What will be the "natural frequency" for an electrical circuit?

Natrual frequency is the same as resonate frequency. Reactive components of a circuit don't dssipate any energy. Circuit capacitance stores electric charge, and transfers that energy into the circuit's inductance. Circuit inductance stores magnetic energy, and transfers that energy into the circuit's capacitance. The process is perpetual. Does that help?

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Try this.

Consider a circuit with R, L and C all in series, an AC supply is connected across the three components, the voltage of the AC supply is fixed at a constant value.

The current flowing through the series circuit will depend on the resistance of the R, the reactance of the L and the reactance of the C.

As the frequency of the AC supply is varied from a low to a high frequency:

the resistance of the R will remain constant,
the reactance of the L will increase,
the reactance of the C will decrease.

At some frequency the the reactance of the L will be the same as the reactance of the C, and because the reactances are of opposite phase they will cancel each other. (Remember in a capacitor the current leads the voltage by 90deg, and in an inductor the current lags the voltage by 90deg hence the voltages are 180deg out of phase when the current is the same in the L and the C, as in a series circuit.)

This frequency is the resonant frequency, and at resonance Xl = -Xc (180deg out of phase) so Xl + Xc = 0.

All that is left to limit the current in our series circuit is the resistance R, so, in a series circuit the impedance is minimum, and the current is maximum at resonance.

I am not sure if this helps or just confuses you more.

JimB

You can also look at resonance from an energy viewpoint. When in resonance the inductive energy is transfered to the capacitor, and then the capacitor transfers the energy back to the inductor in a continuing oscillation. For this to work properly the capacitive energy at maximum capacitor voltage must equal the inductive energy at maximum inductive current. This only occurs when the capacitive reactance equals the inductive reactance, which is the resonant frequency.

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