A capacitor is charged and then made to discharged through a resistance. The time constant is `tau`. In what time will the potential difference across the capacitor decreases by `10%`?

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)e^(-t//tau)`
`V_(C) - q/C = (q_0)/(C ) e^(-t//tau)`
`9/10 (q_0)/(C )= (q_0)/(C ) e^(-t//tau)`
`e^(t//tau) = 10//9 rArr t = tau 1n(10//9)`.