Question Part Points Submissions Used Household electricity in a particular coun
ID: 2892136 • Letter: Q
Question
Question Part Points Submissions Used Household electricity in a particular country is supplied in the form of alternating current that varies from 165 V to 165 V with a frequency of 100 cycles per second (Hz). The voltage is thus given by the equation E(t) = 165 sin(200t) where t is the time in seconds. Voltmeters read the RMS (root-mean-square) voltage, which is the square root of the average value of [E(t)]2 over one cycle. (a) Calculate the RMS voltage of household current in this particular country. (Round your answer to the nearest whole number of volts.)
Explanation / Answer
E(t) = 165 sin(200t)
period =2/(200)
period =1/(100)
in the interval 0t1/100
average value of [E(t)]2 over one cycle
=(1/((1/100)-0))[0 to 1/100][165 sin(200t)]2 dt
=(100)*1652[0 to 1/100][sin(200t)]2 dt
=(100)*1652[0 to 1/100](1/2)[1-cos(400t)] dt
=(50)*1652[0 to 1/100][1-cos(400t)] dt
=(50)*1652[[0 to 1/100][t-(1/400)sin(400t)] ]
=(50)*1652[[(1/100)-(1/400)sin(400/100)]-[0-(1/400)sin(0)]]
=(50)*1652[[(1/100)-0]-0]
=(50)*1652*(1/100)
a)
RMS voltage =[(50)*1652*(1/100)]
RMS voltage =116.67262
RMS voltage =117 volts
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