Question

How many time constants must elapse if an initially charged capacitor is to discharge 90% of its stored energy through a resistor

Answer 1

Answer:

t = log9/10 x RC

Explanation:

Let's say initial energy is

E= 1/2Q²/C

But if 90% is discharged what will be remaining will be

E= E"/100= 1/2Q²/C

So if we divide the first by the second equation we have

Q'= Q/10

Then using

q=q0(1-e^-t /RC)

So that

Q= Q/10(1-e^-t /RC)

t/RC= log9/10

So t = log9/10 x RC