Acapacitor with initial charge q0 is discharged through a resistor. what multiple of the time constant τ gives the time the capacitor takes to lose
(a) the first 1/8-th of its charge
(b)7/8-th of its charge?

a) 0.13*τ ; b) 2.08*τ

Explanation: In order to explain the discharg of a capacitor through a resistor, we have to consider the following:

Q(t)=Qo* exp(-t/τ) for a lose of 1/8-th of its charge

in this case, Q(t)=7/8*Qo=7/8*exp(-t/τ)

ln(7/8)*τ=-t

then, t= -ln(7/8)*τ =0.13

For a lose of 7/8 th  of its charge , we have

Q(t)=1/7*Qo*exp(-t/τ)

t=-ln(1/8)*τ=2.08

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