How many time constans will elapse before a fully charged capacitor loses 99% of its stored charge when connected across a resistor?

Options

A. 1
B. 9.2
C. 4.6
D. 18.4

Answer

C

Explanation

Charge as a function of time in transient state of discharging capacitor is as follows:
`q= q_(0) e^(-t//tau)`
By losing 99% charge we also means that 1% charge is remaining. Hence on substituting `q= 0.01q_(0)` we get the following
`0.01q_(0) = q_(0) e^(-t//tau) rArr e^(t//tau) = 100`
`rArr (t)/(tau) = ln 100 = 4.6 rArr r= 4.6 tau`
Hence option c is correct