tailieunhanh - Electromagnetic Field Theory: A Problem Solving Approach Part 45

Electromagnetic Field Theory: A Problem Solving Approach Part 45. Electromagnetic field theory is often the least popular course in the electrical engineering curriculum. Heavy reliance on vector and integral calculus can obscure physical phenomena so that the student becomes bogged down in the mathematics and loses sight of the applications. This book instills problem solving confidence by teaching through the use of a large number of worked problems. To keep the subject exciting, many of these problems are based on physical processes, devices, and models. This text is an introductory treatment on the junior level for a two-semester electrical engineering. | Magnetic Circuits 415 where k is called the coefficient of coupling. For a noninfinite core permeability k is less than unity because some of the flux of each coil goes into the free space region and does not link the other coil. In an ideal transformer where the permeability is infinite there is no leakage flux so that k 1. From 23 the voltage across each coil is dAi T di i -di2 vi -Li M dt dt dt 26 dA-j .di di2 v2 M Lidl dt dt Because with no leakage the mutual inductance is related to the self-inductances as 27 Ni N2 the ratio of coil voltages is the same as the turns ratio vi dt Ni v2 dk 2ldt N2 In the ideal transformer of infinite core permeability the inductances of 24 are also infinite. To keep the voltages and fluxes in 26 finite the currents must be in the inverse turns ratio 1 2 N 29 The electrical power delivered by the source to coil 1 called the primary winding just equals the power delivered to the load across coil 2 called the secondary winding Vlil v2i2 30 If N2 Ni the voltage on winding 2 is greater than the voltage on winding 1 but current 1 2 is less than i t keeping the powers equal. If primary winding 1 is excited by a time varying voltage Vi t with secondary winding 2 loaded by a resistor RL so that v2 i2RL the effective resistance seen by the primary winding is y M v2 _ M g eff i N2 N2 Ni i2 N2 l 31 32 416 Electromagnetic Induction A transformer is used in this way as an impedance transformer where the effective resistance seen at the primary winding is increased by the square of the turns ratio. c Real Transformers When the secondary is open circuited i2 0 29 shows that the primary current of an ideal transformer is also zero. In practice applying a primary sinusoidal voltage Vocoswt will result in a small current due to the finite self-inductance of the primary coil. Even though this self-inductance is large if the core permeability p. is large we must consider its effect because there is no opposing flux as a result of the open .