I’m a computer engineering student and you remembered correctly, it reaches the final voltage times (1 - 1/e) at the time given by the time constant. Though technically e is the base of an exponential in this case
Mathematically, the thing about e that causes this is the fact that d/dx (ex) = ex. In simpler terms, if a car is driving in a straight line and its speed increases e (2.71) times per second, then its distance travelled always equals its speed (plus some amount that doesn’t change) (ignoring units)
The other cool property about e that I know of relates to complex numbers, but I don’t think I can explain that in a way that’s easy to understand
I’m a computer engineering student and you remembered correctly, it reaches the final voltage times (1 - 1/e) at the time given by the time constant. Though technically e is the base of an exponential in this case
Mathematically, the thing about e that causes this is the fact that d/dx (ex) = ex. In simpler terms, if a car is driving in a straight line and its speed increases e (2.71) times per second, then its distance travelled always equals its speed (plus some amount that doesn’t change) (ignoring units)
The other cool property about e that I know of relates to complex numbers, but I don’t think I can explain that in a way that’s easy to understand