Question

The charge on the capacitor is initially zero, Find the charge on the capacitor as a function of time t. All resistors are of equal value R.

Answer 1

To find time constant of circuit we will have to short circuit the battery, then we will find net resistance across capacitor.

$R_{net}=\frac{R}{2}\therefore {\tau }_C=C{R}_{net}=\frac{CR}{2}$

$\therefore$ Charge in the capacitor at time t would be,

$q=q_o(1-e^{-t/{\tau }_C})=\frac{CE}{2}(1-e^{-\frac{2t}{CR}})$