L-14(NKD)(ET) ((EE)NPTEL) - Module 4 Single-phase AC...

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Unformatted text preview: Module 4 Single-phase AC Circuits Version 2 EE IIT, Kharagpur 1 Lesson 14 Solution of Current in R-L-C Series Circuits Version 2 EE IIT, Kharagpur 2 In the last lesson, two points were described: 1. How to represent a sinusoidal (ac) quantity, i.e. voltage/current by a phasor? 2. How to perform elementary mathematical operations, like addition/ subtraction and multiplication/division, of two or more phasors, represented as complex quantity? Some examples are also described there. In this lesson, the solution of the steady state currents in simple circuits, consisting of resistance R, inductance L and/or capacitance C connected in series, fed from single phase ac supply, is presented. Initially, only one of the elements R / L / C, is connected, and the current, both in magnitude and phase, is computed. Then, the computation of total reactance and impedance, and the current, in the circuit consisting of two components, R & L / C only in series, is discussed. The process of drawing complete phasor diagram with current(s) and voltage drops in the different components is described. Lastly, the computation of total power and also power consumed in the components, along with the concept of power factor, is explained. Keywords : Series circuits, reactance, impedance, phase angle, power, power factor. After going through this lesson, the students will be able to answer the following questions; 1. How to compute the total reactance and impedance of the R-L-C series circuit, fed from single phase ac supply of known frequency? 2. How to compute the current and also voltage drops in the components, both in magnitude and phase, of the circuit? 3. How to draw the complete phasor diagram, showing the current and voltage drops? 4. How to compute the total power and also power consumed in the components, along with power factor? Solution of Steady State Current in Circuits Fed from Single-phase AC Supply Elementary Circuits 1. Purely resistive circuit (R only) The instantaneous value of the current though the circuit (Fig. 14.1a) is given by, t I t R V R v i m m ω sin sin = = = where, I m and V m are the maximum values of current and voltage respectively. Version 2 EE IIT, Kharagpur 3 The rms value of current is given by R V R V I I m m − − = = = 2 / 2 In phasor notation, ) 1 ( j V j V V V + = + = ° ∠ = − ) 1 ( j I j I I I + = + = ° ∠ = − The impedance or resistance of the circuit is obtained as, j R Z I V I V + = ° ∠ = ° ∠ ° ∠ = − − Please note that the voltage and the current are in phase ( ° = φ ), which can be observed from phasor diagram (Fig. 14.1b) with two (voltage and current) phasors, and also from the two waveforms (Fig. 14.1c). In ac circuit, the term, Impedance is defined as voltage/current, as is the resistance in dc circuit, following Ohm’s law. The impedance, Z is a complex quantity. It consists of real part as resistance R, and imaginary part as reactance X, which is zero, as there is no inductance/capacitance. All the components are taken as constant, having linear V-I characteristics. In the three cases being considered, including this one, the power Version 2 EE IIT, Kharagpur 4 consumed and also power factor in the circuits, are not taken up now, but will be...
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This note was uploaded on 08/03/2010 for the course ELECTRICAL EE212 taught by Professor Shetty during the Spring '10 term at International Institute of Information Technology.

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L-14(NKD)(ET) ((EE)NPTEL) - Module 4 Single-phase AC...

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