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# Parallel Resonant Circuits

Connecting an inductor coil and capacitor in parallel results in a *parallel resonant circuit* as illustrated below.

The *conductance* of a parallel circuit comprising a capacitance and inductance is zero when the capacitive and inductive *susceptances* are identical. In this case, the coil and capacitor current are equal and cancel each other out due to their mutual phase displacement of 180°. Consequently, the circuit acts as a pure active resistance *R*_{r} conducting a purely active current *I*_{R}. The right-hand vector diagram below illustrates the *resonant* mode. As in the case of a series resonant circuit, the current *I* at resonance is in phase with the supply voltage *U*. For comparison, the left-hand vector diagram represents a sub-resonant frequency.

At resonance, the coil and capacitor current can therefore attain very high values exceeding the input current by many times.

At resonance, a parallel resonant circuit's resistance attains a maximum and the coil and capacitor experience excessive current (current resonance). |

Because resonance requires inductive and capacitive susceptances to be identical, the resonant frequency is governed by the same equation as for series resonant circuits:

The ratio between either current component and the total current is termed the parallel resonant circuit's quality:

At resonance, each of the two current components is *Q* times the total current. Again using the formula derived previously for series resonant circuits, the quality can be calculated directly based on component parameters.

Parallel resonantcircuits are used, for instance, to filter a certain (resonant) frequency out of a mixture of frequencies. Because the resonant circuit's resistance reaches a maximum at resonance, its amplitude response looks like the following:

This characteristic is inverted as compared to that of a series resonant circuit. Because this kind of filter only allows passage of a particular bandwidth around the resonance frequency, it is termed a *band-pass filter*. Between an antenna and earth, for instance, all the frequencies receivable by the antenna contribute to the output. Connecting a parallel resonant circuit between the antenna and earth effectively short-circuits all frequencies except for the resonant frequency. The voltage source (antenna) therefore operates practically as if it had no load at the resonant frequency and were short-circuited for all other frequencies.