No one has pointed out the one significant aspect of this 'reactance at resonance' issue: it's all a question of phase.
Inductive reactance and capacitive reactance are 180° apart. The magnitudes of those two reactances, at all frequencies except one, will be different: hence, a net reactance will be produced: either capacitive or inductive, depending on which one has the greater magnitude. But when the magnitude of those two reactances are equal, since their phase difference is 180°, the net reactance becomes zero: this occurs at one frequency. At that one critical frequency, the only limiting 'opposition' to the current flowing is the effective total resistive component of that circuit.
This concept is easy to imagine in a series L/C cct. that has resistance in series (real or equivalent) with the capacitance and the inductance. In a parallel L/C cct., the concept is not quite so easy to comprehend. The two reactances are now connected in parallel, not in series, and because of this type of connection, the net reactance at resonance now theoretically approaches infinity. However, since a perfect reactance is impossible to realise in practice (for example, the coil has a real physical resistance), a very high 'opposition' to current flow results. This 'opposition' has all the properties of a real physical resistance, since the supply voltage to, and the supply current in, the L/C cct. are exactly in phase. And the ratio of that voltage and current gives the resultant 'equivalent' resistance: the dynamic resistance of the L/C cct. at resonance. This will automatically include the real 'physical ' resistance of the cct. That dynamic resistance = L/CR, where R = that real resistance. The 'sharpness' of that impedance curve (at resonance only) is assessed by the Q of the cct.: Q = (1/R)*√(L/C).
All of that can be explained much more simply by recourse to some elementary mathematics involving the j operator . . . . but that's another topic for another day.
So there we are. I hope that that little summary of reactance and resonance clears up any confusion here.
Al. / June 12, 2013 //
Inductive reactance and capacitive reactance are 180° apart. The magnitudes of those two reactances, at all frequencies except one, will be different: hence, a net reactance will be produced: either capacitive or inductive, depending on which one has the greater magnitude. But when the magnitude of those two reactances are equal, since their phase difference is 180°, the net reactance becomes zero: this occurs at one frequency. At that one critical frequency, the only limiting 'opposition' to the current flowing is the effective total resistive component of that circuit.
This concept is easy to imagine in a series L/C cct. that has resistance in series (real or equivalent) with the capacitance and the inductance. In a parallel L/C cct., the concept is not quite so easy to comprehend. The two reactances are now connected in parallel, not in series, and because of this type of connection, the net reactance at resonance now theoretically approaches infinity. However, since a perfect reactance is impossible to realise in practice (for example, the coil has a real physical resistance), a very high 'opposition' to current flow results. This 'opposition' has all the properties of a real physical resistance, since the supply voltage to, and the supply current in, the L/C cct. are exactly in phase. And the ratio of that voltage and current gives the resultant 'equivalent' resistance: the dynamic resistance of the L/C cct. at resonance. This will automatically include the real 'physical ' resistance of the cct. That dynamic resistance = L/CR, where R = that real resistance. The 'sharpness' of that impedance curve (at resonance only) is assessed by the Q of the cct.: Q = (1/R)*√(L/C).
All of that can be explained much more simply by recourse to some elementary mathematics involving the j operator . . . . but that's another topic for another day.
So there we are. I hope that that little summary of reactance and resonance clears up any confusion here.
Al. / June 12, 2013 //
