A resonance 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

Options

A. `0.2 s`
B. `0.25s`
C. `25xx10^(-3) s`
D. `2.5xx10^(-3) s`

Answer

D

Explanation

Both V and I are in the same phase. So, let us calculate the time taken by the voltage from peak value to rms value. Now `220=220 sin 100 (pi)t_(1)`.
or, `100 pi (t_1) =(pi)/(2) or (t_1)=(1)/(200)s`
Again, `(220)/(sqrt(2))= 220 sin 100 pi (t_2)`
or `(1) /(sqrt(2))=sin 100 pi (t_2) or 100 pi (t_2) or 100 pi (t_2)= (3 pi)/(4)`
or ` (t_2) =(3)/(400)s`
Required time `=(t_2)-(t_1) =(1)/(400) s =2,5 xx10^(-3) s`.