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Find the effective value of current. i...

Find the effective value of current.
`i=2 sin 100 (pi)t + 2 cos (100 pi t + 30^(@))`.

A

`sqrt(2)A`

B

`2sqrt(2+sqrt(3))`

C

`4`

D

None

Text Solution

Verified by Experts

The correct Answer is:
D
`i_(rms)=sqrt(1/Tint_(0)^(T)i^(2)dt) =sqrt(1/Tint_(0)^(T)(2 sin 100pit+2 sin(100pit+30^(@))^(2)dt))`
`=sqrt(1/Tint_(0)^(T)4 sin^(2) 100pit dt+1/T int_(0)^(T) 4 sin^(2)(100pit+30^(@))dt+1/Tint_(0)^(T)8 sin 100pit sin (100pit+30^(@))dt)`
`=sqrt(4/Tint_(0)^(T) sin^(2) 100 pit dt+4/Tint_(0)^(T) sin^(2)(100pit+30^(@))dt+8/Tint_(0)^(T) sin 100pit sin (100pit+30^(@))dt)`
`=sqrt(4xx1/2+4xx1/2+0)=2 Amp`
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