Chapter 20 - Electric Circuits - Check Your Understanding - Page 569: 22

(e) 0.80s

We know that $\tau = R_{eq} C_{eq}$ In A we have $ R_{eq} =R$ and $\frac{1}{C_{eq}} = \frac{1}{C} +\frac{1}{C} $ $\implies C_{eq} = \frac{C}{2}$ Now, $\tau = R_{eq}C_{eq} \\ 0.20s = R\frac{C}{2}$ $ \implies RC = 0.40s$ In B we have $ R_{eq} = R $ and $C_{eq} = C+C=2C$ $\therefore \tau = R* 2C = 2RC = 2*(0.40s) $ $\implies \tau=0.80s$