An ac generator operates at a rotational frequency of 60 Hz and produces a maxim
ID: 2011668 • Letter: A
Question
An ac generator operates at a rotational frequency of 60 Hz and produces a maximum emf of 100 V. Assume that its output at t = 0 is zero. What is the instantaneous emf (a) at t = 1/240 s ? (b) at t = 1/120 s ? (c) at t ? (d) How much time elapses between successive 0- volt outputs ? (e) What maximum emf would this generator produce if it were operated, instead at 120 Hz ? This is problem number 19, chapter 20, in the College Physics book, seventh edition by Wilson, Buffa, and Lou. Thanks for the help. This is my last question for the day.Explanation / Answer
Given: An ac generator operates at a rotational frequency of f= 60 Hz Thus, Angular frequency = w = 2f = 2(60) = 120 = 376.8 rad/s maximm emf produced = Vmax = 100 volt (a) Since, the sorce is AC , The operating voltage have the form as : V inst = V max sin (wt ) at t = t sec and w = 376.8 rad/s , Vmax = 100 volts V inst =(100) sin ( 376.8x 1/240 ) = (100) sin (1.57 ) = (100) sin (360o x 1.57/6.28) = (100) sin(90o) = 100 (1) = 100 volt (b) V inst = V max sin (wt ) at t = 1/120 sec and w = 376.8 rad/s , Vmax = 100 volts V inst =(100) sin ( 376.8 x 1/120 ) = (100) sin (1.57 rad) = (100) sin (360o x 1.57/6.28) = (100) sin(180o) = 100 (0) = 0 volt (c) V inst = V max sin (wt ) at t = 1/240 sec and w = 376.8 rad/s , Vmax = 100 volts V inst =(100) sin ( 376.8 x t ) = (100) sin (t rad) = (100) sin (360o x t /6.28) = (100) sin(57.32o t ) (d) we have Vmax at t = 1/240 sec as 100 volt Vmax at t= 1/120 sec as 0 volt Thus, Time elapsed between the 0 volt to 100 volt is : 1/ 120 sec - 1/240 sec = 1/240 sec Thus, elepased time : t = 1/240 sec = 0.00417 sec (e ) If f = 120 Hz Vmax = 100 volt (Not depends upon f ) Thus, Angular frequency = w = 2f = 2(60) = 120 = 376.8 rad/s maximm emf produced = Vmax = 100 volt (a) Since, the sorce is AC , The operating voltage have the form as : V inst = V max sin (wt ) at t = t sec and w = 376.8 rad/s , Vmax = 100 volts V inst =(100) sin ( 376.8x 1/240 ) = (100) sin (1.57 ) = (100) sin (360o x 1.57/6.28) = (100) sin(90o) = 100 (1) = 100 volt (b) V inst = V max sin (wt ) at t = 1/120 sec and w = 376.8 rad/s , Vmax = 100 volts V inst =(100) sin ( 376.8 x 1/120 ) = (100) sin (1.57 rad) = (100) sin (360o x 1.57/6.28) = (100) sin(180o) = 100 (0) = 0 volt (c) V inst = V max sin (wt ) at t = 1/240 sec and w = 376.8 rad/s , Vmax = 100 volts V inst =(100) sin ( 376.8 x t ) = (100) sin (t rad) = (100) sin (360o x t /6.28) = (100) sin(57.32o t ) (d) we have Vmax at t = 1/240 sec as 100 volt Vmax at t= 1/120 sec as 0 volt Thus, Time elapsed between the 0 volt to 100 volt is : 1/ 120 sec - 1/240 sec = 1/240 sec Thus, elepased time : t = 1/240 sec = 0.00417 sec (e ) If f = 120 Hz Vmax = 100 volt (Not depends upon f ) at t = 1/120 sec and w = 376.8 rad/s , Vmax = 100 volts V inst =(100) sin ( 376.8 x 1/120 ) = (100) sin (1.57 rad) = (100) sin (360o x 1.57/6.28) = (100) sin(180o) = 100 (0) = 0 volt (c) V inst = V max sin (wt ) at t = 1/240 sec and w = 376.8 rad/s , Vmax = 100 volts V inst =(100) sin ( 376.8 x t ) = (100) sin (t rad) = (100) sin (360o x t /6.28) = (100) sin(57.32o t ) (d) we have Vmax at t = 1/240 sec as 100 volt Vmax at t= 1/120 sec as 0 volt Thus, Time elapsed between the 0 volt to 100 volt is : 1/ 120 sec - 1/240 sec = 1/240 sec Thus, elepased time : t = 1/240 sec = 0.00417 sec (e ) If f = 120 Hz Vmax = 100 volt (Not depends upon f ) (e ) If f = 120 Hz Vmax = 100 volt (Not depends upon f )Related Questions
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