a capacitor in a rc circuit is charged to 60% of its max value in .9 s What is the time constant of the circut

Question

answer is 0.982 s, i just need to know how to do it

Answer 1

Vc=Vmax exp(-t/RC)

60%=Vc/Vmax=exp(-t/RC)=0.6

by taking a ln on both sides we have
ln(Vc/Vmax)=-t/RC

RC= ln(Vmax/Vc)/t (notice the change of sign and Vmax moved to the numerator)

Since now you know RC compute t

t= RC ln(Vmax/Vc)

Answer 2

If the capacitor takes .9s to get to 60% of it's max value, then you must find how many seconds it takes to get to 100% of it's max value.
So set up a conversion and cross multiply...(i.e. 60% is to 0.9s as 100% is to X) (60%/0.9s = 100%/x) or x = 0.9/0.6
So I get the cap taking 1.5 seconds to hit its max value.
In electronics we learned that a cap usually takes 5 time constants to reach max value. That being said, the time constant of a cap that takes 1.5s to charge, will be (1.5s/5) = 0.3s, or 300ms