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3. A diode conducts electric current in one direction but not the other. By putting it in the circuit backwards, it will not conduct. If you crank up the voltage it will eventually fail and let the magic smoke out. When you turn up the reverse voltage on a Zener diode, it will reach a point where it does conduct. Of course, if you turn the voltage up too high the Zener gets hot and melts its important bits just like any other component. 4. A capacitor consists of a dielectric, or insulating layer, and a thin electrode on each side of the dielectric. Of course, you also need terminals to be able to plug the capacitor s electrodes into your circuit. 5. A capacitor does not conduct current, but power can ow through it. A changing electric charge in one of the capacitor s electrodes reaches through the dielectric to wiggle the electrons in the other electrode. This wiggling can do work, but there is no ow of electrons through the capacitor. 6. A resistor and a capacitor can join to make di erent types of AC lters. While there are several answers to the second part of this question, the rst equation used for RC circuits describes the time constant R C.



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Air exhaust (d)

Fig 843: Different types of clean room flows: (a) conventional type of clean-room flow, (b) unidirectional flow,

sinusoidal signal we use the root mean square (RMS) amplitude instead of the raw amplitude: A VRMS p 2 Our 5 V AC signal is equivalent to a 3.5 V DC signal. If we wanted to match the power of our 5 V DC signal we would have to generate a sinusoidal signal that has 7 V peaks.

(c) mixed type of clean-room flow and (d) minienvironment [20]





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with time and the temperature gradient The international reference temperature plays a major role in absolute length measurements However, for relative measurements such as geometrical (form) accuracy and surface roughness measurements, it is enough to have a stable temperature Humidity has an effect on the corrosion of ferrous components, volumetric changes in materials such as granite and composite materials, electrostatic charging, wavelength of lasers as in interferometric measurements and the physical comfort of the personnel Vibrations are caused by excitations through forces from within the machine and from outside through the foundation Vibrations lead to dynamic deformations which cause displacements between the component and the tool or the transducer, leading to erroneous sizes or measurements Vibrations of frequencies above 10 Hz can be easily cut off using commercially available vibration mounts and tables The

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We shall now come to grips with the renormalization operation itself. Let us once again repeat the general ideas and emphasize the outcome of this operation. Our aim is to express the proper Green functions in terms of renormalized Feynman integrals associated with the initial diagrams. This may be achieved by means of three equivalent procedures. In the first approach, the one presented in Chap. 7, we add to the initial lagrangian a formal series (in h) of counterterms. This in turn amounts to an order-by-order redefinition of the parameters of the theory: the "bare" parameters appearing in the lagrangian are implicit functions of the renormalized ones. The former are unobservable and divergent as the regularization is removed, while the latter are the real finite parameters of the theory, mass, coupling constants, etc. Finally, we will see in the next subsections that these two procedures are equivalent to an algorithm of subtraction of the integrand. This operation, due to Bogoliubov, has the merit of providing, diagram by diagram, a finite result without any intermediate recourse to a regularization. We will try to juggle as skilfully as possible with these three equivalent approaches and to use the most appropriate one for each problem. For instance, we shall first discuss the recursive construction of the counterterms and then use the relation between bare and renormalized theories to stress the multiplicative character of the renormalization process. Finally, Bogoliubov's subtraction opera-

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