Household electricity in a particular country is supplied in the form of alterna

Question

Household electricity in a particular country is supplied in the form of alternating current that varies from 175 V to -175 V with a frequency of 30 cycles per second (Hz). The voltage is thus given by the equation E(t) = 175 sin(60 pi t) where t is the time in seconds. Voltmeters read the RMS (root-mean-square) voltage, which is the squareroot 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.) V (b) Many electric stoves require an RMS voltage of 220 V. Find the corresponding amplitude A needed for the voltage E(t) = A sin(60 pi t). A = V

Explanation / Answer

a)
RMs voltage = Eo/sqrt(2)
= 175/sqrt(2)
=124 V
Answer: 124 V

b)
RMS voltage = A/sqrt(2)
220 =A/sqrt(2)
A = 220*sqrt(2)
= 311 V
Answer: 311 V

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