Page:A Treatise on Electricity and Magnetism - Volume 2.djvu/409

778.] resistance of the rest of the system between the electrodes of the condenser, and $$E$$ the electromotive force due to the connexions with the batter.

where $$Q_0$$ is the initial value of $$Q$$.

If $$\tau$$ is the time during which contact is maintained during each discharge, the quantity in each discharge is

By making $$c$$ and $$\gamma$$ in equation (4) large compared with $$\beta$$, $$a$$, or $$\alpha$$, the time represented by $$R_2 C$$ may be made so small compared with $$\tau$$, that in calculating the value of the exponential expression we may use the value of $$C$$ in equation (5). We thus findwhere $$R_1$$ is the resistance which must be substituted for the condenser to produce an equivalent effect. $$R_2$$ is the resistance of the rest of the system, $$T$$ is the interval between the beginning of a discharge and the beginning of the next discharge, and $$\tau$$ is the duration of contact for each discharge. We thus obtain for the corrected value of $$C$$ in electromagnetic measure

778.] If two points of a conducting circuit, between which the resistance is $$R$$, are connected with the electrodes of a condenser whose capacity is $$C$$, then, when an electromotive force acts on the circuit, part of the current, instead of passing through the resistance $$R$$, will be employed in charging the condenser. The current through $$R$$ will therefore rise to its final value from zero in a gradual manner. It appears from the mathematical theory that the manner in which the current through