Capacitance

Two conductors that are not connected and are separated by an insulator constitute a capacitor. When a source of EMF such as a cell is connected to such an arrangement, current flows momentarily, transferring change (in the form of electrons) from one conducting plate (the + plate) to the other (Figure 2.1). When a quantity of charge Q (measured in units of coulombs) has been transferred, the voltage across the plates equals the voltage V across the voltage source. For a fixed arrangement of conductors and insulator, the ratio Q/V is a constant called the capacitance, C. The relationship can be written in the three forms:

with V in volts, Q in coulombs and C in farads.

Figure 2.1: Basic principles of the capacitor. The relationship Q/V shown in the graph, is defined as the capacitance, C.

The parallel-plate capacitor

The parallel-plate capacitor is the simplest theoretical (and practical) arrangement and its capacitance value is, for ideal conditions, easy to calculate. For a pair of parallel plates of equal area A, separation d, the capacitance is given by:

The quantity ?? ₀ is a universal constant called the permittivity of free space, and it has the fixed value of 8.84 10 ^?12 farads per metre. Air has approximately this same value of permittivity also, but other insulating materials have values of permittivity that are higher by the factor ? _r, a...