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Unformatted text preview: Module 4 Singlephase AC Circuits Version 2 EE IIT, Kharagpur Lesson 12 Generation of Sinusoidal Voltage Waveform (AC) and Some Fundamental Concepts Version 2 EE IIT, Kharagpur In this lesson, firstly, how a sinusoidal waveform (ac) is generated, is described, and then the terms, such as average and effective (rms) values, related to periodic voltage or current waveforms, are explained. Lastly, some examples to find average and root mean square (rms) values of some periodic waveforms are presented. Keywords: Sinusoidal waveforms, Generation, Average and RMS values of Waveforms. After going through this lesson, the students will be able to answer the following questions: 1. What is an ac voltage waveform? 2. How a sinusoidal voltage waveform is generated, with some detail? 3. For periodic voltage or current waveforms, to compute or obtain the average and rms values, and also the time period. 4. To compare the different periodic waveforms, using above values. Generation of Sinusoidal (AC) Voltage Waveform R N B ω A S Fig. 12.1 Schematic diagram for single phase ac generation A multiturn coil is placed inside a magnet with an air gap as shown in Fig. 12.1. The flux lines are from North Pole to South Pole. The coil is rotated at an angular speed, n π ω 2 = (rad/s). 2 = n = speed of the coil (rev/sec, or rps) = speed of the coil (rev/min, or rpm) n N ⋅ = 60 l = length of the coil (m) b = width (diameter) of the coil (m) T = No. of turns in the coil Version 2 EE IIT, Kharagpur B = flux density in the air gap ( ) 2 / m Wb n b v π = = tangential velocity of the coil (m/sec) Magnetic Field b A o θ L At a certain instant t, the coil is an angle (rad), t ω θ = with the horizontal (Fig. 12.2). The emf (V) induced on one side of the coil (conductor) is sin v l B , can also be termed as angular displacement. The emf induced in the coil (single turn) is sin 2 sin 2 n b l B v l B = The total emf induced or generated in the multiturn coil is sin sin 2 sin 2 ) ( m E T n b l B n b l B T e = = = This emf as a function of time, can be expressed as, t E t e m sin ) ( = . The graph of or ) ( t e ) ( e , which is a sinusoidal waveform, is shown in Fig. 12.4a Area of the coil b l a m = = ) ( 2 Flux cut by the coil (Wb) = B b l B a = = φ Flux linkage (Wb) = b l B T T = = ψ It may be noted these values of flux and flux linkage , are maximum, with the coil being at horizontal position, = . These values change, as the coil moves from the horizontal position (Fig. 12.2). So, also is the value of induced emf as stated earlier. The maximum value of the induced emf is, dt d n T n T b l B n E m ψψ ωψ πφ = = = = = 2 2 2 Determination of frequency (f) in the ac generator In the above case, the frequency (Hz) of the emf generated is B (a) θ = ω t O M L A N θ (b) Fig. 12.2 (a) Coil position for Fig. 12.1, and (b) Details Version 2 EE IIT, Kharagpur n f = = ) 2 /( π ω , no. of poles being 2, i.e. having only one , no....
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