If an alternating current is given by i = a sin (`omega`t) + b cos (`omega`t), then RMS value of current is :-

Options

A. `a/sqrt2+b/sqrt2`
B. `(a+b)/sqrt2`
C. `sqrt((a^2+b^2)/2)`
D. `(a^2+b^2)/sqrt2`

Answer

C

Explanation

`i=a sin omegat+ bcos omega t` has max value
`=sqrt(a^2+b^2)`
`therefore ` peak value `i_o=sqrt(a^2+b^2)`
`rArr ` RMS value `=i_o/sqrt2=sqrt(a^2+b^2)/sqrt2=sqrt((a^2+b^2)/2)`