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)^(2)+I_(2)^(2))^(1//2)`
B. `(1)/(sqrt(3))(I_(1)^(2)+I_(2)^(2))^(1//2)`
C. `(1)/(sqrt(3))(I_(1)^(2)+I_(2)^(2))^(3//2)`
D. `(1)/(sqrt(3))(I_(1)^(2)+I_(2)^(2))^(3//2)`

Answer

A

Explanation

`I_(rms)=sqrt(overline(I^(2)))`
`=sqrt(overline((I_(1)cosomegat+I_(2)sinomegat)^(2)))`
`=sqrt(I_(1)^(2)overline(cos^(2)omegat)+I_(2)^(2)overline(sin^(2)omegat)+2overline(I_(1)I_(2)sinomegatcosomegat))`
`=sqrt(I_(1)^(2)xx(1)/(2)xxI_(2)^(2)xx(1)/(2)+0)`
`=sqrt((1)/(2)(I_(1)^(2)+I_(2)^(2)))=(1)/(sqrt(2))(I_(1)^(2)+I_(2)^(2))^(1//2)`