Question

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 is
A. `(1)/(4)`
B. `(sqrt3)/(4)`
C. `(1)/(2)`
D. `(1)/(8)`

Answer 1

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`