The electric current in an `AC` circuit is given by `I=I_(0)sin omegat`.What is the time taken by the current to change from its maximum value to the `rms` value?

Answer

`T//8` or `pi/(4omega)`

Explanation

`I_(1)=I_(0)sin omega t_(1)`
`I_(0)=I_(0)sin omega t_(1)`
`t_(1)=(pi//2)/(2pi//T)=T/4`
& `I_(2)=I_(0)/sqrt2=I_(0) sin (omega t_(2))`
`t_(2)=(pi//4)/(2pi//T)=T/8`
`Deltat=t_(1)-t_(2)=T/4-T/8=T/8`