Parallel RLC Resonance and the Tank Circuit
The one point where the susceptances cancel
Sweep the frequency across R, L, C tied in parallel, and the dot on the curve follows the impedance magnitude at that frequency. The capacitor's susceptance ωC grows in proportion to frequency while the inductor's susceptance 1/ωL shrinks in inverse proportion; at resonance ω_0 = 1/√(LC), where the two are exactly equal, they cancel, so the total admittance is at its minimum and the impedance at its maximum (= R). Bring the dot to the resonant frequency, where the dashed line stands, to make the impedance the source sees as large as possible.
In parallel, think in susceptance
Just as reactances added in series, in parallel you add admittances, the reciprocals of impedance, and their imaginary part is called susceptance. An inductor's susceptance is −1/ωL, inversely proportional to frequency, and a capacitor's is +ωC, proportional to it. Their signs are opposite, so adding them subtracts one from the other, and the net susceptance is ωC − 1/ωL. If series resonance was solved by cancelling reactances, parallel resonance is its mirror, the same story solved by cancelling susceptances.
At resonance the impedance is maximal
The frequency where the net susceptance becomes 0, that is, where ωC = 1/ωL, is the resonance point. Solving gives ω_0 = 1/√(LC), the very same formula as series resonance. At this frequency the admittance loses its imaginary part and only the conductance 1/R remains, so it is smallest, the impedance is largest at R, and for the same applied voltage the current the source sends out, V/R, is smallest. If series resonance dropped the impedance to its minimum and threw the circuit wide open, parallel resonance raises the impedance to its maximum and shuts the circuit tight as seen from the source.
A large current circulating in the tank
The source sends out almost no current, but inside the circuit it is not quiet. At resonance the inductor and capacitor have the same voltage across them, and their currents, equal in size and opposite in phase, pass back and forth between them. That circulating current reaches Q times the source current, as energy shuttles between L's magnetic field and C's electric field with almost no leakage. That is why a parallel LC is called a tank circuit and is used in oscillators and RF filters as the key part that holds on to one frequency. If series resonance raised Q times the source voltage across the inductor and capacitor (voltage magnification), parallel resonance circulates Q times the source current inside the tank (current magnification): the two are exact mirrors.
Back to the first screen
As you slid the frequency, the dot on the impedance curve crossed back and forth over the peak, and the top was at ω/ω_0 = 1, that is, at resonance. There the capacitor's ωC and the inductor's 1/ωL became exactly equal, the susceptances cancelled, the admittance reached its minimum, and the impedance reached its maximum, R. The current the source sent out was smallest, yet inside the tank a current Q times larger was circulating between L and C. If series resonance dropped the impedance to its minimum and made the current surge, parallel resonance, its mirror, raises the impedance to its maximum and quiets the source current.