Household electricity is supplied in the form of alternating current that varies

Question

Household electricity is supplied in the form of alternating current that varies from 145 V to 145 V with a frequency of 30 cycles per second (Hz). The voltage is thus given by the equation E(t) below where t is the time in seconds. E(t) = 145 sin (60 pi t) Voltmeters read the RMS (rootmean-square) voltage, which is the squareroot of the average value of [E(t)]^2 over one cycle. Calculate the RMS voltage of household current. Many electric stoves require an RMS voltage of 220 V. Find the corresponding amplitude A needed for the voltage E(t) = A sin (60nt)

Explanation / Answer

here form the equation

Vrms = 0.707 * Vmax

RMS value = maximum value / sqrt (2)

a) Vrms = 0.707 * 145 = 102.515 V

b) Vrms = 0.707 * Vmax

220 / 0.707 = A

A = 311.714 V

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