Capacitance:
Capacitors are devices that store charge. They consist of two plates separated by a dielectric (nonconducting material) and therefore current cannot pass through them. Consequently, they have little use in direct current (DC) circuits. For alternating current (AC) circuits, where the current oscillates (alternates) back and forth a some frequency, they have an effect that appears to be conduction of current. Capacitors are used in camera flash devices, filters, and tuning devices. The definition is:
Thus, the units are coulombs per volt, or C2/J, or C2s2/kg m2. Combinations of units such as this are a nuisance and so we call this particular combination of units the farad (F). Furthermore, it turns out that the farad is too large a unit; we usually work with microfarads, nanofarads, and picofarads (10-12 F). The picofarad has become an industry standard, and capacitors are usually marked with a code that is in picofarads with a power of 10. For example, the digits 394 on a capacitor mean 39 x 104 pF, which is the same as 390 nF or 0.39 microfarads.
Capacitance - dependence on geometry:
As Serway shows in Example 24.8 and on pages 743 and 752 using Gauss' Law, the capacitance of a parallel plate capacitor is dependent on its geometry and the material (dielectric) between the plates:
Sometimes, the product of kappa (the dielectric
constant - see Table 26.1 on page 752) and the permittivity of free space
is
called the permittivity of the material
,
although Serway does not do this. In examples 26.2 and 26.3, Serway derives
expressions for other geometries (cylindrical and spherical).Here's
another example - the Capacitance of a Wire. Figure
26.11 on page 751 shows that the insertion of a dielectric causes the voltage
across the plates to drop for the same amount of charge. This increases
the capacitance since capacitance is inversely proportional to voltage
(see formula above).
Figure 26.12 on page 754 shows three commercial capacitor designs. The first (a) is essentially a parallel-plate capacitor of very large area.
Arrangements of Capacitors:
The simplest combinations are simple series and simple parallel:
Thus, you can see, can't you, that the equivalent capacitance of a parallel network is larger than any one capacitor, whereas the equivalent capacitance of a series network is less than any one capacitor? You can use this to check your work!
For more complex arrangements, you'll need to proceed by reducing the simplest parts first. Please see these examples:
The most commonly used formula, derived on page 750, is:
This result is independent of the geometry. When a capacitor is charged by attaching a battery to the plates, energy is used to create the electric field. When the battery is disconnected and the capacitor shorted out through a resistor (as happens in the flash attachment for a camera), the energy that was stored in the electric field is recovered. (We shall see later that a coil stores energy in its magnetic field and that his can be recovered similarly.)