91Ó°ÊÓ

a) Initial potential difference of the capacitor, $V_0\left(0\right)=100\text{V}$

b) Potential difference at across the capacitor, $V_t\left(10\right)=1.00\text{V}$

c) Time value,$t=17\text{s}$

Using the charging and discharging concept of the capacitor, we can get the required time constant of the RC circuit. Now, for a different time, the discharging as continued, the potential difference will differ and thus is given using the conditions substituted in the voltage formula.

Formulae:

The charge equation of a RC circuit,$q=q_0{e}^{-t/\mathrm{Ï„}}$ (i)

Where,$\mathrm{Ï„}$is the time constant of the RC circuit.

The charge stored within the plates of a capacitor, $q=CV$ (ii)

$$\begin{gathered} V=V_0{e}^{-t/\mathrm{Ï„}}......................\left(a\right) \\ 1=100e^{-10/\mathrm{Ï„}} \\ \mathrm{Ï„}=10\ln \left(100/1\right) \\ =2.17\text{s} \end{gathered}$$

Hence, the value of the time constant is$2.17s$.

At$\mathrm{Ï„}=2.17\text{s}$

$$\begin{gathered} V=100e^{-17/2.17} \\ =100e^{-7.83} \\ =3.96×{10}^{-2}\text{V} \end{gathered}$$

Hence, the value of the potential difference is$3.96×{10}^{-2}\text{V}$.