Page:Electricity (1912) Kapp.djvu/77

Rh fore not permissible to equate potential and e.m.f., but it becomes permissible as a numerical proposition the moment we adopt such a unit for the current, that the product of unit current and unit time equals unit charge in the same system as that adopted in expressing the charge on the sphere. Thus a current of $$i$$ such units, flowing for $$t$$ seconds, corresponds to a charge of $$q$$ units. If the electromotive force required to push these $$q$$ units on to the sphere is denoted by $$e$$ units, then the energy expended is

$$e \times i \times t = eq$$

On the other hand, we know from the definition of the potential that the energy required to bring $$q$$ units from the wall of the room to the sphere requires the energy $$V q$$; and hence it is evident that $$e$$ and $$V$$ are numerically equal. By adopting the system of units here explained, we are therefore justified in considering e.m.f. and potential as numerically equal, and can write

$$e = \frac{Q}{R}$$or$$Q = eR$$

The charge that can be accumulated on a sphere is the product of its radius and the e.m.f. developed by the electric machine. It has been pointed out that the conception