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The instatanteous value of alternating c...

The instatanteous value of alternating current and voltages in a circuit are given as `i=1/(sqrt(2))sin(100pit)` ampere
`e=1/(sqrt(2)) sin (100pit+pi//3)` volt
The average power in watts consumed in the circuit is

A

`1/4`

B

`(sqrt(3))/4`

C

`1/2`

D

`1/8`

Text Solution

Verified by Experts

The correct Answer is:
D
Given equations `i=1/(sqrt(2))sin (100 pit)`
and `e=1/(sqrt(2))sin(100 pit+pi//3)`
`:. i_(0)=1/(sqrt(2))` and `V_(0)=1/(sqrt(2))`
we know that average power
`P_(av)=V_(rms)xxi_(rms) cos phi=1/2xx1/2xxcos 60^(@)`
[`:' i_(rms)=(i_(0))/(sqrt(2))` and `V_(rms)=(V_(0))/(sqrt(2))`]
`=1/2xx1/2xx1/2=1/8 W`
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