seriesPARALLEL RESONANCE CIRCUIT

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SERIES RESONANCE CIRCUIT : - R,L and C in Series: Fig (a) Fig (b) Fig (c)

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ACCEPTER CIRCUIT :-The series R, L and C circuit is called accepter circuit as it accepts or passes the current at resonant freq. At resonance the circuit offers a minimum impedance to the current of resonant freq i.e Z=R and equals the circuit ohmic resistance. The current at this freq is maximum and pass through the circuit easily. That is why it (series resonant circuit) is called accepter circuit. BAND WIDTH : - band width of a tuned circuit is given by the band of freq which lie between two points on either side of its resonance (response) curve where current is Im/  2 or 0.707 of its maximum value at resonance freq.

PARALLEL RESONANCE CIRCUIT: 

PARALLEL RESONANCE CIRCUIT A circuit is said to be in electrical resonance when its capacitive and inductive reactance becomes equal. Consequently net reactance offered by the parallel tuned circuit is maximum for the resonance frequency. A parallel circuit using ideal components is shown in figure below-

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L R Ø L I L I C I R C I C I L Sin Ø L I L I L Cos Ø L V 0 Ø L Ø L X Z

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V L C

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It consists of an ideal resistance less inductor connected in parallel with a perfect capacitor. When frequency of the applied voltage is such that X L becomes equal to X C it becomes a parallel resonant circuit. When the capacitor is removed leaving behind the inductor alone. Let the current drawn the supply be 1 A. when the capacitor is connected back, it also has a current of 1 A flowing through it even though no additional current is taken from the supply! It is found that the current of 1 A drawn by the coil initially keeps alternating or circulating between coil and the capacitor.

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. It is so because there is a phase difference of 180º between the currents drawn by the two. It means that capacitor starts discharging exactly at the instant when coil needs current to build up its magnetic field. Similarly, the coil gives out current exactly when capacitor is ready to charge. In this way the two components keep feeding each other and hence do not draw any current from the supply except for the initial intake. Once drawn, the same current keeps shuttling between L and C even when the circuit is disconnected from the supply. It is sometimes called flywheel effect because it is similar to the action of a mechanical flywheel which once started, tends to keep going indefinitely until stopped by friction or other

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losses. However it should not be forgotten that all this happens when the circuit is in resonance with the supply voltage. Since current drawn from the supply is zero, such an ideal parallel resonant circuit offers infinite resistance to the applied voltage. However, because of some inherent resistance possessed by the coil current is not exactly zero but has a certain minimum value, Consequently impedance offered by such a circuit is maximum and not infinite. A practical circuit is given below –

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L C R

CONDITIONS OF PARALLEL RESONANCE: 

CONDITIONS OF PARALLEL RESONANCE Inductor and capacitor are in parallel. Reactive component of current are equal I C =I L Sin  Circuit impedance is maximum and equal to L/CR and is called dynamic impedance. Line current is I L Cos  and it is in phase with applied voltage. Power factor is unity. It magnifies the current and equals to ωL/R Freq of resonance is equal F 0 = 1  1 - R 2 2   LC L 2 It is known as rejecter circuit because it reject the resonance freq current. It is widely used in amplifier output circuit, oscillator’s filters, freq multipliers and other electronic circuits.

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1. INDUCTIVE SUSCEPTANCE : b=1/X L = 1/2πfL it is inversely proportional to the frequency of the applied voltage. Hence it is represented by a rectangular hyperbola drawn in the fourth quadrant (because it is assumed negative} 2. CAPACITIVE SUSCEPTANCE : B=1/Xc = 2πfC it is increased with the increase in frequency of the applied voltage. Hence it is represented by a straight line drawn in the first quadrant 3. NET SUSCEPTANCE :B it is the difference of the two susceptances and is represented by the dotted hyperbola. At point A the net susceptance is zero.

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4. IMPEDANCE : values of impedance Z are SMALLER for frequencies lower as well as higher than the resonant frequency 5. CURRENT : It varies in exactly the same manner as Y. it has minimum value at resonance and increases for lower as well as higher frequencies.