Give definition and formula of root mean square plot graph of current versus `omega t ` .

Explanation

Root mean square of any physical quantity is called root mean square. In short rms or it is also called effective quatity.
rms current is denoted by I or `I_(rms)` . The graphs of I versus of `omega t ` is given below.

The rms current is related to peak current `I_(m)` by `I = ( I_(m))/( sqrt(2)) = 0.707 I_(m)`
`I_(rms) = sqrt( lt I^(2) gt )`
`= sqrt((1)/(2) I_(m)^(2))`
`= ( I_(m))/( sqrt(2)) = 0.707 I_(m)`
Formula of rms for average power.
`P = bar(p) = ( 1)/(2) I_(m)^(2) R = I_(rms) ^(2) R [ :. (1)/(2) I_(m)^(2) = I_(rms)^(2)]`
and rms value for voltage,
`V = ( V_(m))/( sqrt(2)) = 0.707V_(m)`
Now `V_(m) = I_(m)R ` or `(V_(m))/( sqrt(2)) = ( I_(m))/( sqrt(2)) R ` or `V = IR `. These equations shows the relation between ac voltage and ac current.
For DC voltage relation is given by
`P = (V^(2))/( R ) = VI = I^(2) R `