Question concerning RC Circuits

Question

The capacitor in an RC circuit is discharged with a time constant of 2.00 ms.

(a) At what time after the discharge begins is the charge on the capacitor reduced to half its initial value?

(b) At what time after the discharge begins is the energy stored in the capacitor reduced to half its initial value?

Answer 1

Use the equation

C = Co[e(kt)]

where

C = capacitor charge at any time

Co = initial capacitor charge (before discharge)

k = constant of proportionality = 2 (given)

t = time

The above formula is modified to

C = Co(e^-2t)

NOTE the negative sign attached to the exponent. It means that the  amount of charge in the capacitor is being reduced at any given time "t".

<<  At what time after the discharge begins is the charge on the capacitor reduced to half its initial value? >>

When the capacitor charge is reduced to half of its initial value,

(C/Co) = 0.50 = e^(-2t)

Solving for "t"

ln (0.5) = -2t(ln e) and since ln e = 1,

t = ln (0.5)/(-2)

t = 0.346 seconds

<<  At what time after the discharge begins is the energy stored in the capacitor reduced to half its initial value? >>

I will leave this for you to calculate. I am confident you can figure this out.

Answer 2

idk.