p33_082 - d t 240 ) = 2 A sin 120 2 cos 2 d t 360 2 = 3 A...

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82. (a) We consider the following combinations: ∆ V 12 = V 1 V 2 ,∆ V 13 = V 1 V 3 ,and∆ V 23 = V 2 V 3 . For ∆ V 12 , V 12 = A sin( ω d t ) A sin( ω d t 120 )=2 A sin µ 120 2 cos µ 2 ω d t 120 2 = 3 A cos( ω d t 60 ) where we use sin α sin β = 2 sin[( α β ) / 2] cos[( α + β ) / 2] and sin 60 = 3 / 2. Similarly, V 13 = A sin( ω d t ) A sin( ω d t 240 )=2 A sin µ 240 2 cos µ 2 ω d t 240 2 = 3 A cos( ω d t 120 ) and V 23 = A sin( ω d t 120 ) A sin( ω
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Unformatted text preview: d t 240 ) = 2 A sin 120 2 cos 2 d t 360 2 = 3 A cos( d t 180 ) . All three expressions are sinusoidal functions of t with angular frequency d . (b) We note that each of the above expressions has an amplitude of 3 A ....
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