If you want to find the time constant, you don't need the 0.693
The time constant is just RC
The time constant is the total change divided by the initial rate of change.
For example, 470 :mu:F and 10 k
hm: resistor, time constant is 4.7 s.
If the capacitor is charged to 5 V, the current is 5 / 10000 = 0.5 mA
0.5 mA causes the capacitor to change at 0.0005 / 0.00047 = 1.06 V / second.
Time constant is 5 / 1.06 = 4.7 s, and it doesn't matter what starting voltage you chose.
(Time constants apply to all sorts of things, not just electricity)
Because the voltage falls, the current falls, so the rate of change of voltage also falls. It's called exponential decay.
The formula is V = Vstart * e^(-t/RC)
where V is the voltage on the capacitor
Vstart it what it starts at
e is the mathematical constant = 2.717......
t is the time in seconds
R is the resitance
C is the capacitance
The way that time constants are often measure or used is with "half-lives", or the time to get to half the start value.
If the time to get to half the start value is Th, then:-
0.5 = e^(-Th/RC)
This gives Th/RC = 0.693 and that is where 0.693 comes from.