Electrical Engineering ⇒ Topic : Capacitance of Parallel-Plate Capacitor with Uniform Medium

Capacitance of Parallel-Plate Capacitor with Uniform Medium

We have seen that the capacitance of a capacitor can be determined from its electrical properties using the relation C = Q/V. However, it is often desirable to determine the capacitance of a capacitor in terms of its dimensions and relative permittivity of the dielectric. Although there are many forms of capacitors, the most important an-angement is the parallel-plate capacitor.

Consider a parallel plate capacitor consisting of two plates, each of area A square metres and separated by a uniform dielectric of thickness d metres and relative permittivity 8, as shown in Fig. (A). Let a p.d. of  V volts applied between the plates place a charge of +Q and Q on the plates. With reasonable accuracy, it can be assumed that electric field between the plates is uniform.

                                                              FIGURE (A)

Electric flux density between plates is

                                              D = Q/A coulomb/m²

^{Electric intensity between plates is}

The ratio Q/V is the capacitance C of the capacitor.

The following points may be noted carefully

(1) Capacitance is directly proportional to ε_r and A and inversely proportional to d.

(2)  = = Relative permittivity of medium

(3) Re-arranging the relation for C in air

Obviously, permittivity can also be measured in F/m.