How can i show that the magnitude of the charge on a capacitor is given by...?

Question

Q=Q0(1-e to the square root -t/pie) and Q=Qo e to the square root -t/pie for charging and discharging?

Answer 1

I think you are referring to an RC circuit.

For a charging capacitor
V(t)=Vs(1- e^(-t/(RC)) ) or
V(t)=Vs(1- exp(-t/(RC) )
we know
that Q=CV
then
Q(t)=Qo(1- exp(-t/(RC) )

for discharging
Q(t)=Qo exp(-t/(RC)

Let me know if that helps