The maximum values of the phasors (currents and voltage) in `AC` circuits can be treated as vectors rotating with an angular frequency equal to the angular frequency of the rotor of the generator. If the phase difference between two phasors `vec(A_(1))` and `vec(A_(2))` is `phi` the resultant phasor is :

`A = sqrt(A_(1)^(2) + A_(2)^(2) + 2A_(1)A_(2) cos phi)`
and the phase of `vec(A)` with respects to `A_(1)` is
`beta = "tan"^(-1) (A_(2) sin phi)/(A_(1) + A_(2) cos phi)`
`RHS` value
The rms value of `y = f (t)` is
`y_("rms") = {(int_(0)^(T) [f(t)]^(2) dt)/(T)}^((1)/(2))`
Average value
The average value of `y = f (t)` is `y_(av) = (int_(0)^(T) ydt)/(T)`
Using the above concept, answer the following questions.
The current `i_(1)` and `i_(2)` in `A.C` circuit are given as: `i_(1) = 4 sin (omega t - (pi)/(3))` and `i_(2) = 4 sin (omega t + (pi)/(3))`
The current `i_(3)` can be given as :

Options

A. `4 sqrt(3) sin (omega t - (2 pi)/(3))`
B. `2 sqrt(3) cos (omega t + (pi)/(3))`
C. `4 sin (omega t)`
D. `4 cos (omega t)`

Answer

C