How Does the Time Constant Relate to Charging and Discharging in Capacitors?

[Hannah7h]

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=Q_oe^-t/RC ,time constant is the time taken (when the capacitor is discharging) for charge on a capacitor (Q) to decrease to 37% of Q_o ( 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 Q_o . If this makes any sense, would be good if someone could maybe explain it mathematically as well i.e. how 'e' is involved?

 

[cnh1995]

i.e. how 'e' is involved?

Have you studied calculus?

 

[Hannah7h]

Have you studied calculus?

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

 

[cnh1995]

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.

 

[Hannah7h]

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 Q_o?

 

[cnh1995]

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 0.63Q_o (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]

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.

 

[lychette]

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%

 

[Hannah7h]

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

 

[Hannah7h]

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!