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Household electricity in a particular country is supplied in the form of alternating current that varies from 200 V to −200 V with a frequency of 100 cycles per second (Hz). The voltage is thus given by the equation E(t) = 200 sin(200πt), 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.)
(b) Many electric stoves require an RMS voltage of 220 V.
Find the corresponding amplitude A needed for the voltage E(t) = A sin(200(π)t). (Round your answer to the nearest whole number of volts.)

Answer :

Answer:

a.)  [tex]V_{RMS}[/tex]  = 141 volts

 

b.)  The amplitude A=  1.414 × 220 = 311 volts.

Step-by-step explanation:

The equation of the voltage for the given supply is mentioned as

E(t) = 200 sin(200πt). The equation for a voltage is given by  

 E(t) = [tex]V_{maximum} \times sin(2 \times \pi \times f \times t)[/tex]

where f is the frequency of the supply.

Therefore  [tex]V_{peak}[/tex] (or maximum voltage)= 200 volts.

a.) The RMS voltage can be found from the equation

 [tex]V_{RMS} = \frac{V_{peak}}{\sqrt{2} } = \frac{200}{\sqrt{2} }= 141.42 volts[/tex]

The answer is 141 volts

b. ) It is also mentioned that the requirement for many is an RMS voltage of 220 V.

The corresponding amplitude of the voltage A that is needed will be  

E(t) = Asin(200πt).

We can find A from the expression used in a.) .  

Therefore  

 A =  = 1.414 × 220 = 311 volts.

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