Fundamentals of Materials Science and Engineering: An Integrated Approach, 3e

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12.18 Capacitance • 499

D 0 =  0 

Vacuum  V

V

= l

(a)

l

D 0 =  0  + P

Dielectric P 

V

(b)

Figure 12.28 A

parallel-plate

capacitor (a) when a

vacuum is present

and (b) when a

dielectric material is

present. (From K. M.

Ralls, T. H. Courtney,

and J. Wulff,

Introduction to

Materials Science and

Engineering.

Copyright©c1976 by

John Wiley & Sons,

Inc. Reprinted by

permission of John

Wiley & Sons, Inc.)

capacitance positive to the negative. ThecapacitanceCis related to the quantity of charge stored

on either plateQby^10

C=

Q

V

(12.24)

Capacitance in terms

of stored charge and

applied voltage

whereVis the voltage applied across the capacitor. The units of capacitance are

coulombs per volt, or farads (F).

Now, consider a parallel-plate capacitor with a vacuum in the region between

the plates (Figure 12.28a). The capacitance may be computed from the relationship

C= 0

A

l

(12.25)

Capacitance (for

parallel-plate

capacitor, in a

vacuum)—

dependence on

permittivity of a

vacuum, and plate

area and separation

distance

whereArepresents the area of the plates andlis the distance between them. The

parameter 0 , called thepermittivityof a vacuum, is a universal constant having the

permittivity value of 8.85×^10 −^12 F/m.

(^10) By convention, uppercase “C” is used to represent both capacitance and the unit of
charge, coulomb. To minimize confusion in this discussion, the capacitance designation will
be italicized, asC.