Practicing Success
a b c d |
c |
$\text{Charge in the capacitor at time t } q= q_0 e^{\frac{-t}{RC}}$ $\Rightarrow q = q_0 e^{\frac{-t_2}{RC}} = \frac{q_0}{4}$ $ \Rightarrow \frac{t_2}{RC} = ln4=2ln2 $ $\Rightarrow t_2 = 2ln2 RC$ $U = \frac{U_i}{2}$ $\Rightarrow \frac{1}{2}\frac{q_0^2}{2C} = \frac{q_0^2}{2C} e^{\frac{-2t_1}{RC}}$ $ e^{\frac{-2t_1}{RC}} = \frac{1}{2}$ $\frac{2t_1}{RC} = ln2$ $\Rightarrow t_1 = \frac{ln2}{2} RC$ $\frac{t_1}{t_2} = \frac{1}{4}$ |