Physics - Capacitor Question with Solution | TestHub

Voltage across the capacitors will increase from 0 to $10\mathrm{V}$ exponentially. The voltage at time $t$ will be given by $$\begin{array}{rl}& V=10\left(1-e^{-t/\tau }\mathrm{C}\right)\\ & \text{ Here }{\tau }_c=C_{\text{net }}{R}_{\text{net }}\\ & =\left(1\times 10^6\right)\left(4\times 10^{-6}\right)=4\mathrm{s}\\ & \therefore V=10\left(1-e^{-t/4}\right)\\ & \end{array}$$ Substituting $V=4$ volt we have, $$4=10\left(1-e^{-t/4}\right)$$ Substituting $V=4$ volt we have, $$4=10\left(1-e^{-t/4}\right)$$ or $e^{-t/4}=0.6=\frac{3}{5}$ Taking $\log$ both sides we have, $$-\frac{t}{4}=\ln 3-\ln 5$$ or $t=4(\ln 5-\ln 3)=2\mathrm{s}$. Hence, the answer is 2 .