How Long Does It Take for Half the Energy in a Capacitor to Dissipate?

[PsychonautQQ]

Homework Statement

How long does it take for half the energy stored in a capacitor in an RC circuit to be dissipated?

Homework Equations

dQ(t)/dt = -Q(t)/(RC)

The Attempt at a Solution

So far i know Q(t) = integral(Q(t)/RC)dt
i don't know how to evaluate this integral, and if somebody could guide me through it that'd be awesome, but i know it's suppose to come out to
Q(t) = Qinitial * e^(-t/RC)
and then from there i put Qinitial/2 in for Q(t) and cancel out Qinitials for 1/2 = e-t/RC which would give -RC*ln(1/2) = t but that is not the correct answer ;-( help please

 

[gneill]

Homework Statement

How long does it take for half the energy stored in a capacitor in an RC circuit to be dissipated?

Homework Equations

dQ(t)/dt = -Q(t)/(RC)

The Attempt at a Solution

So far i know Q(t) = integral(Q(t)/RC)dt
i don't know how to evaluate this integral, and if somebody could guide me through it that'd be awesome, but i know it's suppose to come out to
Q(t) = Qinitial * e^(-t/RC)

You start with the differential equation and separate the variables; Gather the Q's on one side and everything else on the other. Both sides can then be integrated separately.

and then from there i put Qinitial/2 in for Q(t) and cancel out Qinitials for 1/2 = e-t/RC which would give -RC*ln(1/2) = t but that is not the correct answer ;-( help please

You're looking for the time when the ENERGY is halved, not the charge. What an expression for the energy stored in a capacitor as a function of charge?

 

[PsychonautQQ]

Thanks. So i figured E is proporation to Q^2 so half the energy must mean that the charge is now Q/(sqrt(2) right?? But following this logic i get RC*ln(sqrt(2) and the answer is supposed to be (RC*Ln(2))/2

Edit: Nevermind, they are equal, haha

 

[gneill]

$ln(\sqrt{2}) = ln(2^{1/2}) = (1/2)ln(2)$