Physics Homework Help?

Question

A capacitor with initial charge q is discharged through a resistor. What multiple of the time constant gives the time the capacitor takes to lose (a) the first one-third of its charge (b) two-thirds of its charge?

Answer 1

The equation for RC circuit is

q=C Vb[1-exp(-t/RC)]



A capacitor with initial charge q is discharged through a resistor. What multiple of the time constant gives the time the capacitor takes to lose (a) the first one-third of its charge (b) two-thirds of its charge?

Qmax= CVb

Then q(t)=Qmax[1-exp(-t/RC)]

(a) the first one-third of its charge
Or q(t)=(1/3)Qmax
So 1-exp(-t/RC)=1/3
exp(-t/RC)=2/3 taking ln on both sides yelds
-t/RC=ln(2/3)
The multiple of the time constant ln(2/3)= -0.41
The multiple is .41
(b)
In this case we solve for
ln(1/3)= -1.1
here it is 1.1