Two alternating voltage generators produce emfs of the same amplitude`(E_0)` but with a phase difference of `(pi)//3`. The resultant emf is

Options

A. `E_(0) sin (omega t + (pi)/(3))`
B. `E_(0) sin (omega t + (pi)/(6))`
C. `sqrt(3) E_(0) sin (omega t + (pi)/(6))`
D. `sqrt(3) E_(0) sin (omega + (pi)/(2))`

Answer

3

Explanation

`E_(1) = E_(0) sin omega t , E_(2) = E_(0) sin (omega t + pi//3)`
`E = E_(2) + E_(1)`
`E_(0) sin (omega t + pi//3) + E_(0) sin omega t`
`= 2 E_(0) sin (omega t + pi//6) cos (pi//6)`
`= sqrt(3) E_(0) sin (omega t + pi// 6)`