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In a circuit, the instantaneous values of alternating current and voltages in a circuit is given by `I = (12)/(sqrt2) sin (100 pi t) A` and `E = (1)/(sqrt2) sin (100 pi t + (pi)/(3)) V`. The average power in watts consumed in the circui isA. `(1)/(4)`B. `(sqrt3)/(4)`C. `(1)/(2)`D. `(1)/(8)` |
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Answer» Correct Answer - D Here, on comparing with `I = I_(0) sin omega t ` and `E = E_(0) sin (omega t + phi)` we get `I_(0) = 1//sqrt2 A` `E_(0) = 1//sqrt2 V` `phi = (pi)/(3)` `E_(upsilon) = (E_(0))/(sqrt2) = (1 //sqrt2)/(sqrt2) = (1)/(2) V`, `I_(upsilon) = (I_(0))/(sqrt2) = (1 //sqrt2)/(sqrt2) = (1)/(2) A`, `cos phi = "cos" (pi)/(3) = (1)/(2)` `P_(av) = E_(upsilon) I_(upsilon) cos phi = ((1)/(2)) ((1)/(2)) ((1)/(2)) = (1)/(8) W` |
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