A resistance of `20 Omega` is connected to a source of an alternating potential `V=220 sin (100 pi t)`. The time taken by the current to change from the peak value to rms value is

Explanation

Let current at t = 0 is zero and increasing in positive direction then current as a function of time can be written as follows : `i=i_(0) omegat_(1)`
`implies sin omegat_(1)=1 `
`implies t_(1) = (pi)/(2omega)`
Let time taken to reach rms value from zero be`t_(2)` . We can write the following :
`(i_(0))/(sqrt(2))= i_(0) sin omegat_(2)`
`implies sin omegat_(2) =(1)/(sqrt(2))`
`implies t_(2) = (pi)/(4omega) `
Time taken by the current to attain a value of `i_(0)` from `(i_(0))/(sqrt(2))` or to attain a value of `(i_(0))/(sqrt(2))` from `i_(0)` can be written as difference of the two above - calculated time intervals. Hence time taken by the current to attain rms value starting from its peak value can be written can be written as follows :
`t=t_(1)-t_(2)= (pi)/(2omega)-=(pi)/(4omega) = (pi)/(4omega)`
`implies t =(pi)/(4xx2pixx50)= 2.5xx10^(-3)s`
` implies t = 2.5 ` ms