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We understand that different materials vary widely in the resistance they offer to the flow of electricity, and can guess that with any given material long piece will offer more resistance than a short piece, and a thin piece than a thick. We have indeed actually proved as 34 much and more; by the rule for resistances in series the resistance of a uniform wire is exactly proportional to its length—doubling the length is equivalent to adding another equal resistance in series, and so on (Fig. 13a).

LOOVy 100 ν t t t î t M (α) ,'ι + ί ί i Ί jTi i Ί Ί Ί 1i1 11 ί i l ί1 ! 1 i i ι ι ι 1 ι ι ι ι ι I ι " ιοον ' oov ι (b) (c) Fig. 3 Consideration of the electric field between closely spaced parallel plates leads to the relationship between dimensions and capacitance Suppose, for the sake of example, the plates are charged to 100V. Since the field is uniform, the potential changes at a uniform rate between one plate and the other. Reckoning the potential of the lower plate as zero, the potential half way between the plates is therefore + 50V.

As with written symbols, facility in drawing and reading circuit diagrams soon comes with practice. One warning is needed in connection with circuit diagrams, especially when going on to more advanced work. They are an indispensably convenient aid to thought, but it is possible to allow one's thoughts to be moulded too rigidly by them. The diagram takes for granted that all electrical properties are available in separate lumps, like chemicals in bottles, and that one can make up a circuit like a prescription.