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As shown in Figure 41, the capacitance of a parallel-plate capacitor is given by the expression A d where is the permittivity of the dielectric material, A the area of each of the plates, and d their separation The permittivity of air is 0 = 8854 10 12 F/m, so that two parallel plates of area 1 m2 , separated by a distance of 1 mm, would give rise to a capacitance of 8854 10 3 F, a very small value for a very large plate area This relative inef ciency makes parallel-plate capacitors impractical for use in electronic circuits On the other hand, parallel-plate capacitors nd application as motion transducers, that is, as devices that can measure the motion or displacement of an object In a capacitive motion transducer, the air gap between the plates is designed to be variable, typically by xing one plate and connecting the other to an object in motion Using the capacitance value just derived for a parallel-plate capacitor, one can obtain the expression C= C= 8854 10 3 A x

where C is the capacitance in pF, A is the area of the plates in mm2 , and x is the (variable) distance in mm It is important to observe that the change in capacitance caused by the displacement of one of the plates is nonlinear, since the capacitance varies as the inverse of the displacement For small displacements, however, the capacitance varies approximately in a linear fashion The sensitivity, S, of this motion transducer is de ned as the slope of the change in capacitance per change in displacement, x, according to the relation dC 8854 10 3 A pF = dx 2x 2 mm Thus, the sensitivity increases for small displacements This behavior can be veri ed by plotting the capacitance as a function of x and noting that as x approaches zero, the slope of the nonlinear C(x) curve becomes steeper (thus the greater sensitivity) Figure 46 depicts this behavior for a transducer with area equal to 10 mm2 S= This simple capacitive displacement transducer actually nds use in the popular capacitive (or condenser) microphone, in which the sound pressure waves act to displace one of the capacitor plates The change in capacitance can then be converted into a change in voltage or current by means of a suitable circuit An extension of this concept that permits measurement of differential pressures is shown in simpli ed form in Figure 47 In the gure, a three-terminal variable capacitor is shown to be made up of two xed surfaces (typically, spherical depressions ground into glass disks and coated

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200 150 C (pF) 100 50 0 1

Figure 9-12. Choosing a location and language In the Location combo box, you will see three choices: File System, HTTP, and FTP. Both HTTP and FTP allow you to create a new website directly on a web server. The only web server that .NET supports is Microsoft s IIS. So, in order to use either the FTP or HTTP options, IIS must be installed on either your own desktop PC, another server on your network, or a server at an Internet Service Provider (ISP) where you have an account. To make web development easier, Microsoft now provides a built-in web server with all of the Visual Web Developer 2005 Editions. This greatly simplifies development and is a welcome addition. To use this feature, choose the File System option in the Location combo box and specify not a web server s name but a folder on the local hard drive. Visual Studio will use this folder to store your web files while you are developing them, and the built-in web server will treat your application just as if it were on an IIS server. This lets you easily browse and debug the application as you develop it. When you are done with the development of your website, you can simply copy, or upload as it is called, your files to an actual production web server.

5 6 x (mm)

Appendix B:

Thin deflecting plate Fixed surfaces vS (t) + _ R2 c c b d d R1 a_

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