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# Resonance in parallel rlc circuit

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Presentation on parallel resonance for b-tech 1st year...

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### Resonance in parallel rlc circuit

1. 1. Seminar On Basic Electrical Engineering(TEE-201) Topic: Parallel Resonance Made By: Shivam Gupta Roll No.-33 Sec.-E
2. 2. Contents Parallel Resonance • Parallel Resonance Introductio n • Introduction Parallel RLC Circuit • Parallel RLC Circuit Resonant Frequency • Resonant Frequency Parallel Resonant Circuit • Parallel Resonant Circuit Frequency Curve • Frequency Curve Impedence Of a Parallel Resonant Circuit • Impedence Of a Parallel Resonant Circuit Current In Parallel Resonant Circuit • Current In Parallel Resonant Circuit Susceptanc e Of a Parallel Resonant Circuit • Susceptance Of a Parallel Resonant Circuit Bandwidth Of a Parallel Resonant Circuit • Bandwidth Of a Parallel Resonant Circuit Review • Review
3. 3. PARALLEL RESONANCE The resonance that results when circuit elements are connected with their inductance and capacitance in parallel, so that the impedance of the combination rises to a maximum at the resonant frequency.
4. 4. INTRODUCTION • The resonant electrical circuit must have both inductance and capacitance. • In addition, resistance will always be present due either to the lack of ideal elements or to the control offered on the shape of the resonance curve. • When resonance occurs due to the application of the proper frequency ( fr), the energy absorbed by one reactive element is the same as that released by another reactive element within the system.
5. 5. Resonant Frequency  The frequency at which the inductive and capacitive reactances of a parallel resonant circuit are equal.  The frequency at which the parallel impedance of a parallel resonant circuit is maximum.  The frequency at which the parallel impedance of a parallel resonant circuit has a power factor of unity.
6. 6. Calculation Of Resonant Frequency Simple parallel resonant circuit (tank circuit). Since we know the equations for determining the reactance of each element at a given frequency, and we're looking for that point where the two reactances are equal to each other, we can set the two reactance formulae equal to each other and solve for frequency algebraically.
7. 7. XL=2πfL XC=1/2πfC Resonance occurs when XL = XC
8. 8. This is a formula to tell us the resonant frequency of a tank circuit, given the values of inductance (L) in Henrys and capacitance (C) in Farads.
9. 9. Phasor diag. for parallel resonant circuit.
10. 10. Parallel resonant circuits • A parallel resonant circuit is resistive at the resonant frequency.At resonance XL=XC, the reactive components cancel. The impedance is maximum at resonance. • Below the resonant frequency, the parallel resonant circuit looks inductive since the impedance of the inductor is lower, drawing the larger proportion of current. • Above resonance, the capacitive rectance decreases, drawing the larger current, thus, taking on a capacitive characteristic.
11. 11. Capacitive Frequency Curve For Parallel Resonance Resistive Inductive
12. 12. Impedence Of A Parallel Resonant Circuit Impedance is maximum at resonance in a parallel resonant circuit, but decreases above or below resonance. Voltage is at a peak at resonance since voltage is proportional to impedance (E=IZ). Impedance peaks at resonance
13. 13. Current In A Parallel Resonance Circuit At resonance the current flowing through the circuit is at its minimum as the inductive and capacitive branch currents are equal ( IL = IC ) and are 180o out of phase.
14. 14. We remember that the total current flowing in a parallel RLC circuit is equal to the vector sum of the individual branch currents and for a given frequency is calculated as:
15. 15. At resonance, currents IL and IL are equal and cancelling giving a net reactive current equal to zero. Then at resonance the above equation becomes.
16. 16. Susceptance At Resonance  The inductive susceptance, BL is inversely proportional to the frequency as represented by the hyperbolic curve. The capacitive susceptance, BC is directly proportional to the frequency and is therefore represented by a straight line. The final curve shows the plot of total susceptance of the parallel resonance circuit versus the frequency and is the difference between the two susceptances.
17. 17. At the resonant frequency point were it crosses the horizontal axis the total circuit susceptance is zero.
18. 18. Bandwidth Of A Parallel Resonant Circuit BW = Δf = fh-fl = 343-281 = 62 fl = fc - Δf/2 = 312-31 = 281 fh = fc + Δf/2 = 312+31 = 343 Q = fc/BW = (312 Hz)/(62 Hz)=5 The bandwidth of the parallel resonant response curve is measured between the half power points. This corresponds to the 70.7% voltage points since power is proportional to E2. ((0.707)2=0.50) Since voltage is proportional to impedance, we may use the impedance curve.
19. 19. Review: • At resonance parallel RLC circuit acts like an open circuit. • Current at resonance is at it’s minimum. • Impedence of the parallel resonant circuit is maximum and is equal to the resistance.This resistance is known as dynamic resistance. • Susceptance At resonant frequency is equal to ZERO
20. 20. THE END THANK YOU