Household electricity in a particular country is supplied in

Household electricity in a particular country is supplied in the form of alternating current that varies from 170 V to 170 V with a frequency of 90 cycles per second (Hz). The voltage is thus given by the equation E(t) = 170 sin(180t) 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.) 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(180t). (Round your answer to the nearest whole number of volts.) A = V

Solution

a)

Maximum Voltage

E_max=170 Volts

Rms Voltage

E_Rms=E_max/sqrt[2] =170/sqrt2

E_Rms=120.2 Volts =120 Volts (approx)

b)

Amplitude or maximum Voltage

A =sqrt[2]*E_Rms =sqrt[2]*220

A=311.1 Volts =311 Volts (approx)