The voltage across and the current through a load are expressed as follows v(t)=-170 \sin (377 t-\frac{\pi}{6}) V i(t)=8 \cos (377 t+\frac{\pi}{6}) A The average power in watts (round off to one decimal place) consumed by the load is___________ W.

GATE Electrical Engineering (EE) 2019 Solved Paper

Question : 36 of 65

Marks: +1, -0

The voltage across and the current through a load are expressed as follows

v(t)=-170 \sin (377 t-\;{π}/{6}) V

i(t)=8 \cos (377 t+\;{π}/{6}) A

The average power in watts (round off to one decimal place) consumed by the load is___________ W.

Solution:

{V}=-170 \sin (377 {t}-30^{∘})

=-(170 ∠-30^{∘})

I=8 \cos (377 t+30^{∘})

=8 \sin (90^{∘}+377 {t}+30^{∘})

=+(8 ∠ 120^{∘})

{S}^{*}= {VI}^{*}=-(\;{170}/{√{2}} ∠-30^{∘})(\;{8}/{√{2}}<-120^{∘})

{S}^{*}=-(680 ∠-150^{∘})

{S}^{*}=-(-588.89- {j} 340)

{S}^{*}=588.89+ {j} 340

{P}_{ {avg}}=588.89 {W}

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