The rms value of emf is given by `E (8 sin omega t + 6 cos omega t)` volt is

Options

A. `5 sqrt2V`
B. `7sqrt2V`
C. 10V
D. `10 sqrt2V`

Answer

A

Explanation

`E = (8 sin omega t + 6 cos omega t) = (A cos theta sin omega t - A sin theta cos omega t)`
where, `A cos theta = 8 and A sin theta = 6`.
`A^(2) (cos^(2) theta + sin^(2) theta) = 8^(2) + 6^(2) = 100`
A =10
rms value, `E_(rms) = (A)/(sqrt2) = (10)/(sqrt2) = (5 xx 2)/(sqrt2) = 5 sqrt2`