what is the use of series and parallel resonance?

Answer 1

If you are referring to electrical circuits, then mathematically, there is no difference. There might be some practical difference, but I never heard of it.

Electric motors are inductive (they are an electromagnet), which means they are drawing current during a half cycle of A/C voltage (to charge their magnetic field) and they are discharging during the other half cycle as the magnetic field collapses due to the current changing direction. When the magnetic field collapses, the energy has to go somewhere, so it is turned into a back flow of current in the system that interferes with the current in the wire and gets wasted as heat. One solution is to place a capacitor in the circuit that will charge as the motor is discharging, and vice versa. The extra power is stored in the capacitor during the half cycle that the motor is discharging, and the capacitor's discharge is used to automatically recharge the inductor during the other half cycle. Saves energy (called power factor correction).

The same principle can be used to tune filters to allow only certain frequencies to pass -- like in a TV or radio tuner -- you only want one channel at a time (the resonant frequency will pass through). Since your speakers are inductors, the right size capacitor with determine if the speaker is a wolfer (low pass) or a tweeter (high pass).

Answer 2

Series and parallel resonance can all be considered parallel resonance. The configuration of the circuit generally has a series resistance (from the inductor if nothing else) There might be a parallel resistance, or the equivalent if energy is coupled out of the circuit. Sometimes an intentional resistance is used to make sure the quality (Q) of energy loss per cycle of oscillation remains constant. The coupling to external circuits looks like a parallel resistance.
The previously mentioned "Q" is defined as the loss per oscillation cycle. Q of 100 loose 1% of energy per cycle. Series circuits are sometimes used to supply large amounts of current into a small load resistance. Quartz crystals have the equivalent of an incredibly large inductor in series with a small capacitor. Because of the natural configuration, they are sometimes sold with "Series resonant" frequency. At the same time, the package (case) of the crystal has capacitance, which resonates with the crystal to form a parallel resonant frequency very close to the parallel resonant frequency. For this reason, crystals used in oscillators where the series resonance (Pierce oscillators for instance) use series resonance specifications, where crystals that are used in lightly coupled circuits using parallel resonance generally specify parallel resonance frequency.

Quartz crystal equivalent circuit
http://www.ieee-uffc.org/freqcontrol/quartz/vig/vigequiv.htm

series tunes crystal oscillator circuit
http://my.integritynet.com.au/purdic/crystal-oscillators.htm

parallel resonant crystal oscillator circuit
http://my.integritynet.com.au/purdic/crystal-oscillators.htm

Hope this helps