# Time constant and capacitors

So the rate at which a capacitor charges and discharges is dependent on resistance in a circuit and the magnitude of capacitance of the capacitor? So the time constant is equal to RC. So using this equation where Q=Qoe-t/RC ,time constant is the time taken (when the capacitor is discharging) for charge on a capacitor (Q) to decrease to 37% of Qo ( i.e. charge on the capacitor when it is is fully charged). But I've been reading around and what I don't get is how the time constant is also equal to the time taken for the charge (Q) on a charging capacitor to increase by 63% of Qo . If this makes any sense, would be good if someone could maybe explain it mathematically aswell i.e. how 'e' is involved?

cnh1995
Homework Helper
Gold Member
i.e. how 'e' is involved?
Have you studied calculus?

Have you studied calculus?

Um haven't studied it in much detail, but I could give it a go

cnh1995
Homework Helper
Gold Member
Um haven't studied it in much detail, but I could give it a go
Well, KVL equation for an RC circuit is a differential equation. Solving that differential equation, you get exponential expressions for charge, current and voltage.

Well, KVL equation for an RC circuit is a differential equation. Solving that differential equation, you get exponential expressions for charge, current and voltage.

Ok so... how does this relate to the 63% of Qo?

cnh1995
Homework Helper
Gold Member
time constant is the time taken (when the capacitor is discharging) for charge on a capacitor (Q) to decrease to 37% of Qo
Or in other words, time taken to lose 63% of Q0.
on a charging capacitor to increase by 63% of Qo
You can see that the time taken to gain a charge of 0.63Qo (while charging) is equal to the time taken to lose the same charge of 0.63Q0(while discharging). It's obvious, isn't it?

cnh1995
Homework Helper
Gold Member
Ok so... how does this relate to the 63% of Qo?
If you are asking where 63% comes from, it comes from the constant 'e-1' in the solution to the differential equation of the RC circuit.

the time constant is the time taken to get to within 37% of the final value.
In decay the final value is 0%!
In growth the final value is 100%

If you are asking where 63% comes from, it comes from the constant 'e-1' in the solution to the differential equation of the RC circuit.

Ok that was pretty obvious now I look at it, thank you for explaining it otherwise I probably wouldn't have got there lol

the time constant is the time taken to get to within 37% of the final value.
In decay the final value is 0%!
In growth the final value is 100%

Yep this makes sense, thanks!