Question

At time t = 0, a battery of 10 V is connected across points A and B in the given circuit. If the capacitors have no charge initially, at what time (in seconds) does the voltage across them become 4 V? [Take: In 5 = 1.6, In 3 = 1.1]

Answer 1

$\therefore$ In the given figure, $R_{eq}=1M\Omega ,C_{eq}=4\mu F$

Time constant, $\tau =R_{eq}{C}_{eq}=4s$

Potential across the equivalent capacitor at any time t is

$V=V_0(1-e^{-t/\tau })$

$4=10(1-e^{-t/4})$

$\frac{t}{4}=In\left(5\right)=In\left(3\right)=1.6-1.1=0.5\Rightarrow t=2s$.