L-17(NKD)(ET) ((EE)NPTEL)

# L-17(NKD)(ET) ((EE)NPTEL) - Module 4 Single-phase AC...

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Module 4 Single-phase AC Circuits Version 2 EE IIT, Kharagpur

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Lesson 17 Resonance in Series and Parallel Circuits Version 2 EE IIT, Kharagpur
In the last lesson, the following points were described: 1. How to compute the total impedance in parallel and series-parallel circuits? 2. How to solve for the current(s) in parallel and series-parallel circuits, fed from single phase ac supply, and then draw complete phasor diagram? 3. How to find the power consumed in the circuits and also the different components, and the power factor (lag/lead)? In this lesson, the phenomenon of the resonance in series and parallel circuits, fed from single phase variable frequency supply, is presented. Firstly, the conditions necessary for resonance in the above circuits are derived. Then, the terms, such as bandwidth and half power frequency, are described in detail. Some examples of the resonance conditions in series and parallel circuits are presented in detail, along with the respective phasor diagrams. Keywords : Resonance, bandwidth, half power frequency, series and parallel circuits, After going through this lesson, the students will be able to answer the following questions; 1. How to derive the conditions for resonance in the series and parallel circuits, fed from a single phase variable frequency supply? 2. How to compute the bandwidth and half power frequency, including power and power factor under resonance condition, of the above circuits? 3. How to draw the complete phasor diagram under the resonance condition of the above circuits, showing the currents and voltage drops in the different components? Resonance in Series and Parallel Circuits Series circuit C E L A R D + - I B V frequency (f) Fig. 17.1 (a) Circuit diagram. The circuit, with resistance R, inductance L, and a capacitor, C in series (Fig. 17.1a) is connected to a single phase variable frequency ( ) supply. f The total impedance of the circuit is Version 2 EE IIT, Kharagpur

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+ = C L j R Z ω ωφ 1 where, f R C L C L R Z πω ωω φ 2 ; ) / 1 ( tan ; 1 1 2 2 = = + = The current is () = ° = Z V Z V I / 0 where [] 2 1 2 2 / 1 ( C L R V I + = The current in the circuit is maximum, if C L 1 = . The frequency under the above condition is C L f o o π 2 1 2 = = This condition under the magnitude of the current is maximum, or the magnitude of the impedance is minimum, is called resonance. The frequency under this condition with the constant values of inductance L, and capacitance C, is called resonant frequency. If the capacitance is variable, and the frequency, is kept constant, the value of the capacitance needed to produce this condition is f L f L C 2 2 ) 2 ( 1 1 = = The magnitude of the impedance under the above condition is R Z = , with the reactance , as the inductive reactance 0 = X L X l = is equal to capacitive reactance C X C / 1 = . The phase angle is ° = 0 , and the power factor is unity ( 1 cos = ), which means that the current is in phase with the input (supply) voltage. . So, the magnitude of the current ( ) / ( R V ) in the circuit is only limited by resistance, R. The phasor diagram
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L-17(NKD)(ET) ((EE)NPTEL) - Module 4 Single-phase AC...

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