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Unformatted text preview: soidal steady state at time t is given by p ( t ) = v ( t ) i ( t ) , where the voltage v ( t ) and current i ( t ) are given by v ( t ) = V m cos ω t , i ( t ) = I m cos ( ω t + φ ) , for some constants V m , I m , ω , and φ . Show that the instantaneous power can be written as p ( t ) = 1 2 V m I m cos φ + 1 2 V m I m cos (2 ω t + φ ) . Solution: By deFnition of p ( t ), we have p ( t ) = V m I m cos ω t cos ( ω t + φ ) = V m I m · 1 2 (cos (2 ω t + φ ) + cos ( − φ )) (by formula (3.43)) = 1 2 V m I m cos φ + 1 2 V m I m cos (2 ω t + φ ) (since cos ( − φ ) = cos φ ) ....
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This note was uploaded on 01/21/2012 for the course MAC 1130 taught by Professor Dr.cheun during the Fall '11 term at FSU.
 Fall '11
 Dr.Cheun
 Calculus

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