Page:Elementary lectures on electric discharges, waves and impulses, and other transients (Steinmetz 1911).djvu/21

 the second case, of current $$i'$$, at the moment $$t_1$$; that is, from $$t$$ onward, curve $$i$$ is the same as curve $$i'$$ from time $$t_1$$ onward. Since

$$i'$$ is proportional to $$i$$ from any point $$t$$ onward, curve $$i'$$ is proportional to the same curve $$i$$ from $$t_1$$ onward. Hence, at time $$t_1$$, it is

or,

where $$c = -\frac{1}{i_1} \frac{di_1}{dt} = \mbox{constant}$$, and the minus sign is chosen, as $$\frac{di}{dt}$$ is negative.

As in Fig. 4: