Question

At time $t=0$, a battery of $10V$ 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 becomes 4 volt? $[$ take $ln5=1.6,ln3=1.1]$

Answer 1

Equation of charging of capacitor

$V=V_0(1-e^{\frac{-t}{R_{eq}{C}_{eq}}})$

$R_{eq}=\frac{2\times 2}{2+2}=1M\Omega$

$C_{eq}=2+2=4\mu F$

$V=V_0(1-e^{\frac{-t}{4}})$ where $V_0=10V$ and $V=4V$

$\Rightarrow 4=10(1-e^{\frac{-t}{4}})$

$\Rightarrow e^{\frac{-t}{4}}=\frac{3}{5}$

$\Rightarrow \frac{t}{4}=ln5-ln3$

$\Rightarrow t=2sec$