tailieunhanh - Basic Theoretical Physics: A Concise Overview P17

Basic Theoretical Physics: A Concise Overview P17. This concise treatment embraces, in four parts, all the main aspects of theoretical physics (I . Mechanics and Basic Relativity, II. Electrodynamics and Aspects of Optics, III. Non-relativistic Quantum Mechanics, IV. Thermodynamics and Statistical Physics). It summarizes the material that every graduate student, physicist working in industry, or physics teacher should master during his or her degree course. It thus serves both as an excellent revision and preparation tool, and as a convenient reference source, covering the whole of theoretical physics. It may also be successfully employed to deepen its readers’ insight and. | 160 19 Maxwell s Equations I Faraday s and Maxwell s Laws where i2 1 we thus have UG t Re UGeiwt and I t Re Jeiwt where U uG0 and J I 0 e-ia . By analogy with Ohm s law we then define the complex quantity R where UG R I. The quantity R is the complex . resistance or simply impedance. The total impedance of a circuit is calculated from an appropriate combination of three types of standard elements in series or parallel etc. 1. Ohmic resistances positive and real are represented by the well-known rectangular symbol and the letter R. The corresponding complex resistance is Rr R . 2. Capacitive resistances negatively imaginary correspond to a pair of capacitor plates together with the letter C. The corresponding impedance is given by Rc i A short justification UC t Cl . UC t Cpr Thus with the ansatz UC t k e - one obtains UC t GUC t . 3. Inductive resistances positively imaginary are represented by a solenoid symbol together with the letter L. The corresponding impedance is Rl CL . The induced voltage drop in the load results from building-up the magnetic field according to the relation UL t L t . UL t L I t . But with the ansatz I t k e - we obtain I t CI t . One can use the same methods for mutual inductances . transformers see exercises 5. 5 The input load voltage of the transformer is given by the relation uT iwLi 2 J2 while the output generator voltage is given by uT An J1. Applications Complex Resistances etc. 161 d An . resonance circuit The following is well-known as example of resonance phenomena. For a series RLC circuit connected as a load to an alternating-voltage generator UG t U 0 cos ut one has 1 1 U R Thus we obtain R i uL 1 -1 uC I t I 0 cos ut a with I 0 11 uL t- vr and tan a R uL - R For sufficiently small R see below this yields a sharp resonance at the resonance frequency 1 uo . Vl C For this frequency the current and the voltage are exactly in phase whereas for higher frequencies the current is delayed with respect to the .