Consider the RC circuit shown in the figure. What will be the final charge $Q_{\infty }$ and the equivalent time constant of the circuit.

 

In steady state, current through each branch is $\frac{E}{3R}.$ The final potential difference across the  capacitor is  $(\frac{E}{3R}.2R -\frac{E}{3R}.R) i.e.\frac{E}{3}.$ $E/3.\text{ So }Q=CE/3$

$R_{\text{eff }}=4R/3\Rightarrow \tau =R_{eff}\times C=4RC/3$