I would have given you something from my self-refresher courses in Lie groups and manifolds with topological spaces but I would rather have my “equation of the weekend” taken from my other technical stuffs like this one. This, one of the many amazing things I never cease to be fascinated about, especially conservation (conversion) laws.

Now about this, one can notice that a loaded electric generator may experience transient acceleration or transient change of kinetic energy per unit time the moment it begins supplying electrical power to an external load resistance. The acceleration of the moving conductor dies out may be quickly in time as the velocity of the conductor settles down to a constant value. How soon the transient quantities die out depends variably on the total resistance, which in turn may vary with the external load resistance.

While when an open circuit (infinite resistance) condition is approached that is, electric power is vanishing, the acceleration tends to persist infinitely longer in time and as this happens the velocity ceases to be dependent on the resistance. Instead, the velocity increases linearly with time, given an open circuit in which electric power is no longer expended from the generating conductor.