Determine the power and RMS value of
the following signals y(t ) = 5cos(50t+3)
Answers
Given : y(t ) = 5cos(50t+3)
To Find : RMS Value
Solution:
(RMS Value)² = (1/π) ∫(5cos(50t+3))² .dt
=> (RMS Value)² = (1/π) ∫25cos²(50t+3)) .dt
cos²(50t+3) = (1 + Cos2(50t + 3))/2
=> (RMS Value)² = (1/π) ∫25( (1 + Cos2(50t + 3))/2) .dt
=> (RMS Value)² = (25/2π) ∫dt + (25/2π)Cos (100t + 6)) .dt
=> (RMS Value)² = (25/2π) t + (25/2π)Sin (100t + 6)/100
t = 0 to π
=> (RMS Value)² = (25/2π) π + (25/2π)Sin (100π + 6)/100 - (25/2π)Sin (6)/100
=> (RMS Value)² = (25/2) + (25/2π)Sin (6)/100 - (25/2π)Sin (6)/100
=> (RMS Value)² = (25/2) + 0
=> (RMS Value)² = (25/2)
=> RMS Value = 5/√2
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Answer:
explain with signal and also find Power