Find the effective value of current.
`i=2 sin 100 (pi)t + 2 cos (100 pi t + 30^(@))`.

Options

A. `sqrt(2)A`
B. `2sqrt(2+sqrt(3))`
C. 4
D. `2sqrt(2)A`

Answer

A

Explanation

Equation can be written as `i=2 sin 100 pit+2 sin(100pit+120^(@))`
so phase difference `phi=120^(@)`
`=sqrt(A_(1)^(2)+A_(2)^(2)+2A_(1)A_(2)cos phi)`
`=sqrt(4+4+2xx2xx2(-1/2))=2` so effective value will rms. Value =`2//sqrt(2)=sqrt(2)A`