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Resonance occurs when the reactance of an inductor balances the reactance of a capacitor at some given frequency. In such a resonant circuit where it is in series resonance, the current will be maximum and offering minimum impedance. In parallel resonant circuits the opposite is true.
The formula for resonance is:
2 * pi * f * L = 1 / (2 * pi * f * C)
where: 2 * pi = 6.2832; f = frequency in hertz L = inductance in Henries and C = capacitance in Farads
Which leads us on to:
f = 1 / [2 * pi (sqrt LC)]
where: 2 * pi = 6.2832; f = frequency in hertz L = inductance in Henries and C = capacitance in Farads
A particularly simpler formula for radio frequencies (make sure you learn it) is:
LC = 25330.3 / f ^{2}
where: f = frequency in Megahertz (Mhz) L = inductance in microhenries (uH) and C = capacitance in picofarads (pF)
Following on from that by using simple algebra we can determine:
LC = 25330.3 / f ^{2} and L = 25330.3 / f ^{2} C and C = 25330.3 / f ^{2} L
In a series resonant circuit the impedance is at its lowest for the resonant frequency whereas in a parallel resonant circuit the impedance is at its greatest for the resonant frequency. See figure 1.
Figure 1  resonance in series and parallel circuits
"For a series circuit at resonance, frequencies becoming far removed from resonance see an ever increasing impedance. For a parallel circuit at resonance, frequencies becoming far removed from resonance see an ever decreasing impedance".
That was a profoundly important statement. Please read it several times to fully understand it.
A typical example to illustrate that statement are the numerous parallel circuits used in radio. Look at the parallel resonant circuit above. At resonance that circuit presents such a high impedance to the resonant circuit to the extent it is almost invisible and the signal passes by. As the circuit departs from its resonant frequency, up or down, it presents a lessening impedance and progressively allows other signals to leak to ground. At frequencies far removed from resonance, the parallel resonant circuit looks like a short path to ground. For series resonance the opposite is true.
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Updated 15th May, 2000