Capacitance Definition and Calculation

A capacitor s proportionality constant refers to its capacitance, and provides a measurement of the amount of charge necessary to induce a specified potential between the plates. The magnitude of capacitance is independent of the charge accumulated across the plates in a linear capacitor. However, this capacitance is dependent upon the geometry of the charged plates. Capacitance is measured in farads (F) where 1 F = 1 coulomb/volt (C/V). Combining Equations (1.10) and (1.11), capacitance can be expressed as 

Equation (1.12) demonstrates that capacitance is dependent on the dielectric constant of the dielectric material, the electrode surface area, and the distance between the two planar electrodes. However, Equation (1.12) is applicable 

For a spherical capacitor with an iimer sphere radius of a and an outer sphere radius of b, its capacitance is 

For an isolated sphere capacitor that only has a single isolated spherical conductor with a radius of R, its capacitance can be expressed as 

Equations (1.12) through (1.15) demonstrate that capacitance is strongly dependent on the dielectric constant Sq if the configuration of the capacitor is fixed. This eg is the dielectric constant of an empty vacuum. However, for a non-vacuum dielectric, the material s relative permittivity or relative dielectric constant is defined as the relative dielectric constant (e, = e/eq) where e is the dielectric constant of the material. Note that this equation will be discussed further in Section 1.3.1. Every dielectric material has a different dielectric constant resulting in a different capacitance. Table 1.1 lists the dielectric constants of common materials used in capacitors. All of them have larger dielectric constants compared to those of air or a vacuum. In this case. Equation (1.12) can be rewritten as 

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