Can the instantaneous power output of an ac source ever be negative ? Can the average power output be negative ?

Answer

A

Explanation

Let the applied emf
`E= E_(0)sinomegat`
and current developed is
`I=I_(0)sin(omegat+- phi)`
Instantaneous power output of the AC source
`P=EI = (E_(0)sinomegat)` `[I_(0)sin(omegat+-phi)]`
`=E_(0)I_(0)sinomegat.sin(omegat+phi)`
`=(E_(0)I_(0))/2[cosphi-cos(2omegat+phi)]` ...............(i)
Average power
`P_(av) = V_(0)/sqrt(2) I_(0)/sqrt(2) cosphi`
`=V_(rms)I_(rms)cosphi`..................(ii)
Where `phi` is the phase difference.
Clearly, from eq.(i)
when `cosphi lt cos(2omegat+phi)`
Yes, the instantaneous power output of an AC source can be negative.
From eq. (ii)
`P_(av)gt0`
Because `cosphi = R/Z gt0`
No, the negative power ouput of an AC source cannot be negative.