Some clocks that are powered by an AC voltage use the AC frequencyto keep time.

Question

Some clocks that are powered by an AC voltage use the AC frequencyto keep time. The power company makes this possible by arranging tohave precisely the correct number of cycles occur every day, whichkeeps such clocks from gaining or losing time over long periods. (a) How many cycles of AC voltage are thereeach month (31 days) in the UnitedStates?
1 cycles

(b) Suppose a clock designed for the United States (where the ACfrequency is 60 Hz) is taken to a different country where thefrequency is 50 Hz. After one fullmonth (31 days) at its new location,this clock will be in error by an amount t. Findt.
2 s
(a) How many cycles of AC voltage are thereeach month (31 days) in the UnitedStates?
1 cycles

(b) Suppose a clock designed for the United States (where the ACfrequency is 60 Hz) is taken to a different country where thefrequency is 50 Hz. After one fullmonth (31 days) at its new location,this clock will be in error by an amount t. Findt.
2 s

Explanation / Answer

a) the number of cycles N in one month is a product of thattime period t and frequency f N= t f t= 31 x 24 x 3600 = 2678400 s f= 60 Hz (or s-1) N= t f= 2678400 x 60=160704000 cycles b) In this case since t= N/f then t=t50 -t60 t=   N/f50 -N/f60 = N( 1//f50 - 1/f60) t= 535680 s t= 148.8hours since t= N/f then t=t50 -t60 t=   N/f50 -N/f60 = N( 1//f50 - 1/f60) t= 535680 s t= 148.8hours

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