Find rms value in the following cases
(a) `I = 5 +3 sin omegat`
(b) ` I = a sin omegat + b cos omegat`
(c ) `I =i_(1) sin omegat + i_(2) cos omegat + i_(3) sin 2 omegat` .

Explanation

`bari^(2)= (int_(0)^(T) i^(2)dt)/(int_(0)^(T) dt) = (1)/(T) int_(0)^(T) (5 + 3sin omegat)^(2)dt`
`= (1)/(T) int_(0)^(T) (25 + 30sin omegat + 9sin^(2) omegat)dt`
`= (1)/(T) [25 T + 30 int_(0)^(T) sin omegat dt + 9 int_(0)^(T) sin^(2) omega dt]`
`(1)/(T) [25T + 0 + 9 .(T)/(2)] =25+ (9)/(2) =5^(2) + (3^(2))/(2)`
`i_(rms) = sqrt(bari^(2)) = sqrt(5^(2) + (3^(2))/(2) ) =sqrt59/(2)`
`bar(i^(2))=(a^(2))/(2) + (b^(2))/(2)`
`i _(rms) = sqrt((a^(2) +b^(2))/(2))`
`bar(i^(2))=(i_(1)^(2))/(2) + (i_(2)^(2))/(2) + (i_(3)^(2))/(2)`
`i_(mas) = sqrt((i_(1)^(2) + i_(2)^(2) +i_(3)^(2))/(2))` .