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Can the instantaneous power output of an ac source ever be negative ? Can the average power output be negative ? |
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Answer» Solution :Let the applied EMF, `E=E_m sin OMEGAT` and current DEVELOPED is, `I=I_m sin (omegatpmphi)` (Here E is taken INSTEAD of V) Instantaneous power output of the AC source, P=EI `=E_m sin omegat xx I_m sin (omegat + phi)` `=(E_m I_m)/2 [2 sin omegat sin (omegat+phi)]` `=(E_m I_m)/2 [cos phi - cos (2omegat+phi)]` .....(1) [`because` 2sinAsinB=cos(A-B) -cos(A+B)] (i) from equation (1), If cos `phi lt cos (2omegat+phi)`, then P `lt` 0 mean negative power `therefore` Yes, the instantaneous power output of an AC source can be negative . `therefore` Average power `lt P gt =V_m/sqrt2 I_m/sqrt2 cos phi` `lt P gt =V_"rms" I_"rms" cos phi`...(2) where `phi` is phase difference . (ii) and from equation (2) `lt P gt gt 0` because cos`phi=R/Z gt 0` No, the average power output of an AC source cannot be negative . |
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