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Chapter18 Capacitance
Capacitor is a device you can use to store energy as potential energy in an electric field. Capacitors also have many other uses in our electronic and microelectronic age. They are vital elements in the circuits with which we turn radio and television transmitters and receivers. Microscopic capacitors form the memory banks of computers.
18.1 Capacitance
1.The left figure shows some of the many sizes and shapes of
capacitors. The right figure shows the basic elements of any
capacitor-two isolated conductors of arbitrary shape. No matter what their geometry, flat or not, we call these conductor plates.
2.The following figure shows a less general but more
conventional arrangement, called a parallel-plate capacitor,
consisting of two parallel
conducting plates of area A
separated by a distance d.
The symbol that we use to
represent a capacitor is based
on the structure of a
parallel-plate capacitor but is used for capacitors of all geometries.
3.When a capacitor is charged, its plates have equal but
opposite charge of +q and –q. However, we refer to the charge of a capacitor as being q, the absolute value of these charges on the plates.
4.Because the plates are conductors, they are equipotential
surfaces: all points on a plate are at the same electric potential.
Moreover, there is a potential difference between the two plates. For historical reasons, we represent the absolute value of this potential difference with V.
5.The charge q and the potential difference V for a capacitor are
proportional to each other, That is, CV
q . The proportionality constant C is called the capacitance of the capacitor. Its value depends only on the geometry of plates and not on their charge or potential difference.
6. The SI unit of capacitance is coulomb per volt. This unit occurs so often that it is given a special name, the farad (F). The farad is a very large unit.
Submultiples of the farad, such as the
microfarad (F F 6101-=μ) and the
picofarad (F pF 12101-=), are more
convenient units in practice.
7. Charging a Capacitor: See right
figure.
18.2 Calculating the capacitance
1. There are four steps to calculate the capacitance of a capacitor:
(1) assume a charge q on the plates; (2) calculate the electric field E between the plates in terms of this charge, using
Gauss ’ law; (3) knowing E , calculate the potential difference
V between the plates ⎰-
+=Eds V , in which the + and – remind
us that our path of integration starts on the positive plate and ends on the negative plate; (4) calculate C.
2. A parallel-plate capacitor : (1)
A q σ= (2) 0εσ=E (3) 0εσd
Ed V == (4) d
A d A V q C 00)/(εεσσ===. So the capacitance does indeed depend only on geometrical factors .
