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

Options

A. `tau 1n (0.1)`
B. `tau 1n (0.9)`
C. `tau 1n 10/9`
D. `tau 1n 11/10`

Answer

C

Explanation

`q = q_(0) (1-e^(-t//tau))`
`1/10 q_(0)=q_(0) (1-e^(-t//tau))implies e^(-t//tau) = 9/10`
`e^(-t//tau)=10//9`
`t/(tau) 1n e = 1n(10//9)`
`t=tau 1n(10//9)`.