Consider the sinusoidal voltage v= 170cos( 120pi t-60 degree) V what is the firs
ID: 1797925 • Letter: C
Question
Consider the sinusoidal voltage v= 170cos( 120pi t-60 degree) V what is the first time after t=0 that v= 170V? The sinusoidal function is shifted 125/18 ms to the left along the time axis. What is the expression for v(t)? What is the minimum number of milliseconds that the function must be shifted to the right if the expression for v(t) is 170 sin 120 pi t V? What is the minimum number of milliseconds that the function must be shifted to the left if the expression for v(t) is 170 cos 120 pi t V?Explanation / Answer
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60o = /3 .
a) Now at 120t = /3 the v = 170cos(0) = 170V
Therefore , t = (1/360)s = (25/9)ms.
b) = 120 = 2(f) gives f = 60Hz.
T = 1/f = (1000/60)ms = (50/3)ms.
Phase difference added = 360o(125/18)/(50/3) = 150o.
v = 170cos(120t + 90o).
c) cos( - 270) = sin.Therefore it should be shifted right by 210o.
t = (50/3)(7/6)/2 = 175/18 ms.
d) It should be shifted by 60o .Thus
t = (50/3)(/3)/2 = 50/18 = 25/9 ms.