Question

A capacitor charges from a cell through a resistance. The time constant is T. in what time will the capacitor collect 10% of the final charge ?

• A. $\tau In\left(0.1\right)$
• B. $\tau In\left(0.9\right)$
• C. $\tau In\frac{10}{9}$
• D. $\tau In\frac{11}{10}$

Answer 1

Answer: (C)

$\tau In\frac{10}{9}$

As we know,

$Q=Q_0(1-e^{-t/\tau })$

$\Rightarrow Q_0/10=Q_0(1-e^{-t/\tau })$

or $e^{-t/\tau }=0.9$

$\Rightarrow e^{t/\tau }=10/9$

$\Rightarrow t=\tau \ln \left(\frac{10}{9}\right)$