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

Answer

C

Explanation

`I=I_(1)cos omegat+I_(2)cos omegat`
`(I^(2))=mean=I_(1)^(2)bar(cos^(2)omegat)+I_(2)^(2)bar(sin^(2)omegat)`
`+2I_(1)I_(2) bar(cos omegat.sin omegat)`
`= I_(1)^(2).(1)/(2) +I_(2)^(2).(1)/(2)+2I_(1)I_(2)xx0`
`I_(r.m.s)=((I_(1)^(2)+I_(2)^(2))^(1//2))/(sqrt(2))`