Question

The charge flown through a circuit in the time interval between t and t+dt is given by $dq=e^{-t/\tau }dt$, where $\tau$ is a constant. Find the toatal charge flown through the circuit t = 0 to t = $\tau$

• A. $\tau (\frac{1}{e}-1)$
• B. $\tau (1-\frac{1}{e})$
• C. $\tau (1+\frac{1}{e})$
• D. None of these

Answer 1

The correct option is B

$\tau (1-\frac{1}{e})$

Solution: The total charge flown is the sum of all the dq's for t varying from t = 0 to $t=t_0$. Thus, the total charge flown is

$Q=\underset{0}{\overset{\tau }{\int }}{e}^{-t/t}dt$

=$[\frac{e^{-t/\tau }}{-1/\tau }{]}_0^{\tau }=\tau ⟮1-\frac{1}{e}⟯$