An AC is given by the equation `i=i_(1)cos omegat+i_(2)sin omegat`. The r.m.s. current is given by

Options

A. `(1)/(sqrt(2))(i_(1)+i_(2))`
B. `(1)/(sqrt(2))(i_(1)+i_(2))^(2)`
C. `(1)/(sqrt(2))(i_(1)^(2)+i_(2)^(2))^(1//2)`
D. `(1)/(2)(i_(1)^(2)+i_(2)^(2))^(1//2)`

Answer

C

Explanation

As We know,
`i_(rms)=sqrt(i_(1)^(2)+i_(2)^(2))((i_(1))/(sqrt(i_(1)^(2)+i_(2)^(2)))cosomegat+(i_(2))/(sqrt(i_(1)^(2)+i_(2)^(2)))sinomegat)`
`I_(rms)=(I_(0))/(sqrt(2))`
i.e. `i_(rms)=sqrt((i_(1)^(2)+i_(2)^(2))/(2))=(1)/(sqrt(2))(i_(1)^(2)+i_(2)^(2))^(1//2)`