The figure shows an experimental plot for discharging of a capacitor in an $$R-C$$ circuit. The time constant $$\tau$$ of this circuit lies between:

$$Q = c\varepsilon_0 e^{-tcR}$$

$$4\varepsilon = 4\varepsilon_0 \varepsilon^{-t\tau}$$

$$\varepsilon = \varepsilon_0 \varepsilon^{-t\tau}$$

When $$t = 0 \implies \varepsilon_0 = 25$$

$$\varepsilon = \varepsilon_0 = 25$$

When $$t = 200 \implies \varepsilon = 5$$

$$5 = 25 e^{-\frac{200}{\tau}}$$

$$\ln 5 = e^{-\frac{200}{\tau}}$$

$$\tau = \frac{200}{\ln 5} = \frac{200}{\ln 10 - \ln 2}$$

$$= \frac{200}{\ln 10 - 0.693}$$