#### Transcript Electro Mechanical System

Chapter 9 Ideal Transformer Lecture 04 Electro Mechanical System 1 Ideal Transformer Introduction Transformers are one of the most useful electrical devices ever invented. It can raise or lower the voltage or current in an ac circuit. It can isolate circuits from each other. It can change the apparent value of impedance. The transformer enables us to transmit electrical energy over great distances. Lecture 04 Electro Mechanical System 2 Eelements of transformer Lecture 04 Electro Mechanical System 3 Transformer application Lecture 04 Electro Mechanical System 4 Voltage Induction For a coil consisting of N turns placed in a variable flux , the flux alternates sinusoidally at a frequency f, periodically reaching positive and negative max. The flux induces a sinusoidal ac voltage. d e(t ) N dt The rms valueof voltageE is given by E 2fN max E 4.44 fN max Where: E = effective voltage induced [V] f = the frequency of flux [Hz] N = number of turns. max is the peak value of flux [Wb] (The reason for using peak flux is that it is proportional to peak flux density Bmax which in iron cores, determine the value of saturation.) Lecture 04 Electro Mechanical System 5 Applied Voltage & Induced Voltage Consider a coil connected across an AC voltage source Eg. The coil and source resistances are negligible. The induced voltage E must equal the source voltage Eg. A sinusoidal AC flux must exist to generate the induced voltage on the N turns of the coil. max varies in proportion to Eg. Placing an iron core in the coil will not change the flux . Eg 4.44 fN max max Lecture 04 Eg 4.44 fN Electro Mechanical System 6 Applied Voltage & Induced Voltage Magnetization current Im drives the AC flux The current is 90° out-of-phase and lagging with respect to the voltage. To produce the same flux a smaller magnetomotive force is needed with an iron core than an air core. Less magnetizing current is required. So with an iron core, less current is needed to drive the AC flux. Lecture 04 Electro Mechanical System 7 Applied Voltage & Induced Voltage Example A coil, having 4000 turns, links an AC flux with a peak value of 2mWb at a frequency of 60 Hz Calculate the rms value of the induced voltage What is the frequency of the induced voltage? E = 4.44 f N max E = 4.44 x 60 x 4000 x 0.002 E = 2131 V The induced voltage has rms value of 2131 V and a frequency of 60 Hz. The peak voltage is: 2131 x √2 = 3014 V Lecture 04 Electro Mechanical System 8 Applied Voltage & Induced Voltage Example: A coil, having 90 turns, is connected to a 120 V, 60 Hz source the rms magnetization current is 4 A. Find: a) Peak value of the flux. c) Inductive reactance of the coil. Eg 120 0.005 5m Wb 4.44 60 90 a) Φmax b) I max 2 I 2 4 5.66A 4.44 fN b) Peak value the mmf. d) Inductance of the coil. P eak mmf U NIm 90 5.66 509.1A (T heflux is equal t o 5mWbat an inst ant when coil mmf is 509.1ampere- t urns) E g 120 30 c) X m 4 Im d )L Lecture 04 Xm 30 0.0796 79.6m H 2 60 2f Electro Mechanical System 9 Elementary Transformer Consider an air-core coil, excited by an AC source Eg, draws a magnetization current Im, produces a total flux A second coil is brought close to the first a portion m1 of the flux couples the second coil, the mutual flux an AC voltage E2 is induced the flux linking only the first coil is called the leakage flux, f1 Improved flux coupling concentric windings, iron core weak coupling causes small E2 Lecture 04 Electro Mechanical System 10 Elementary Transformer The magnetization current Im produces both fluxes m1 and f1 The fluxes are in-phase The voltages Eg and E2 are in-phase Terminal orientation such that the coil voltages are inphase and are said to possess the same polarity Lecture 04 Electro Mechanical System 11