L> Resonant RLC CircuitsResonance

Resonance in AC circuits indicates a distinct frequency identified by the worths of the resistance , capacitance , and inductance . For series resonance the condition of resonance is straightforward and also it is defined by minimum impedance and zero phase. Parallel resonance , i beg your pardon is an ext common in digital practice, needs a much more careful definition.

You are watching: In an lrc circuit, when the inductive and capacitive reactances are equal,

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Go BackSeries Resonance

The resonance that a series RLC circuit occurs once the inductive and capacitive reactances room equal in magnitude however cancel every other since they space 180 degrees apart in phase. The spicy minimum in impedance which occurs is helpful in tuning applications. The sharpness that the minimum relies on the value of R and also is identified by the "Q" that the circuit.

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Detailed expressions
Calculation
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Go BackSelectivity and Q the a Circuit

Resonant circuits are provided to answer selectively to signal of a offered frequency when discriminating versus signals of various frequencies. If the response of the circuit is more narrowly peaked roughly the liked frequency, us say that the circuit has higher "selectivity". A "quality factor" Q, as defined below, is a measure of the selectivity, and we speak that a circuit having a "high Q" if the is an ext narrowly selective.

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An instance of the application of resonant circuits is the choice of am radio station by the radio receiver. The selectivity of the tuning need to be high sufficient to discriminate strongly against stations above and below in carrier frequency, but not therefore high regarding discriminate versus the "sidebands" developed by the imposition that the signal through amplitude modulation.

The selectivity the a circuit is dependent top top the lot of resistance in the circuit. The sports on a series resonant circuit at appropriate follow an instance in Serway & Beichner. The smaller sized the resistance, the greater the "Q" for provided values the L and also C. The parallel resonant circuit is much more commonly used in electronics, however the algebra vital to characterize the resonance is much much more involved.

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Using the same circuit parameters, the illustration at left shows the power dissipated in the circuit together a role of frequency. Due to the fact that this power depends upon the square the the current, these resonant curves show up steeper and also narrower than the resonance peaks for current above.

The quality element Q is characterized by

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where Δω is the width of the resonant power curve at half maximum.
Since the width transforms out to it is in Δω =R/L, the value of Q can also be expressed as

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The Q is a typically used parameter in electronics, through values normally in the range of Q=10 to 100 because that circuit applications.IndexAC CircuitsReferenceSerway & BeichnerCh 33
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Go BackPower in a series Resonant Circuit

The median power dissipated in a collection resonant circuit deserve to be expressed in terms of the rms voltage and also current together follows:

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Using the develops of the inductive reactance and also capacitive reactance, the term entailing them can be to express in regards to the frequency.

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where use has actually been make of the resonant frequency expression
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Substitution now gives the expression for average power as a duty of frequency.
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This power circulation is plotted at left making use of the very same circuit parameters as were used in the instance on the Q element of the series resonant circuit

The median power at resonance is simply

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since in ~ the resonant frequency ω0 the reactive components cancel so the the circuit appears as simply the resistance R.

IndexAC CircuitsReferenceSerway & BeichnerCh 33
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