Basic AC Reactive Components
RESONANCE
RESONANCE
In the chapters on inductance and capacitance we have learned that
both conditions are reactive and can provide opposition to current flow,
but for opposite reasons. Therefore, it is important to find the point
where inductance and capacitance cancel one another to achieve
efficient operation of AC circuits.
EO 1.15
DEFINE resonance.
EO 1.16
Given the values of capacitance (C) and inductance (L),
CALCULATE the resonant frequency.
EO 1.17
Given a series R-C-L circuit at resonance, DESCRIBE
the net reactance of the circuit.
EO 1.18
Given a parallel R-C-L circuit at resonance, DESCRIBE
the circuit output relative to current (I).
Resonant Frequency
Resonance occurs in an AC circuit when inductive reactance and capacitive reactance are equal
to one another: XL = XC. When this occurs, the total reactance, X = XL - XC becomes zero and
the impendence is totally resistive. Because inductive reactance and capacitive reactance are both
dependent on frequency, it is possible to bring a circuit to resonance by adjusting the frequency
of the applied voltage. Resonant frequency (fRes) is the frequency at which resonance occurs, or
where XL = XC. Equation (8-14) is the mathematical representation for resonant frequency.
(8-14)
fRes
1
2p LC
where
fRes
= resonant frequency (Hz)
L
= inductance (H)
C
= capacitance (f)
Series Resonance
In a series R-C-L circuit, as in Figure 9, at resonance the net reactance of the circuit is zero, and
the impedance is equal to the circuit resistance; therefore, the current output of a series resonant
circuit is at a maximum value for that circuit and is determined by the value of the resistance.
(Z=R)
I
VT
ZT
VT
R
Rev. 0
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