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Integration problem about household electricity

  1. Sep 19, 2005 #1

    Stevecgz

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    I don't understand what the following problem is asking for:

    Household electricity is supplied in the form of alternating current that varies from 155 V to -155 V with a frequency of 60 cycles per second (Hx). The voltage is thus given by the equation:

    [tex]E(t) = 155\sin(120\pi t)[/tex]

    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 [tex][E(t)]^2[/tex] over one cycle.

    a. Calculate the RMS voltage of household current.

    b. Many electric stoves requre an RMS voltage of 220 V. Find the corresponding amplitude A needed for the voltage [tex]E(t)=A\sin(120\pi t)[/tex].

    If someone could explain to me what they are asking for it would be appreciated.

    Steve
     
    Last edited: Sep 19, 2005
    Stevecgz, Sep 19, 2005
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  3. Sep 19, 2005 #2

    George Jones

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    Use an integral to calculate to calculate the average

    [tex]
    A = \frac{1}{T} \int_{0}^{T} E \left( t \right)^2 dt,
    [/tex]

    where [itex]T[/itex] is the time taken for one period, and then take the square root to find the RMS value of the voltage.

    Working from right to left, RMS means: first square [itex]E[/itex], then take the average, then take the square root.

    Regards,
    George
     
    George Jones, Sep 19, 2005
  4. Sep 19, 2005 #3

    George Jones

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    Staff Emeritus
    Science Advisor
    Gold Member

    Use an integral to calculate to calculate the average

    [tex]
    A = \frac{1}{T} \int_{0}^{T} E \left( t \right)^2 dt,
    [/tex]

    where [itex]T[/itex] is the time taken for one period, and then take the square root to find the RMS value of the voltage.

    Working from right to left, RMS means: first square [itex]E[/itex], then take the average, then take the square root.

    Regards,
    George
     
    George Jones, Sep 19, 2005
  5. Sep 20, 2005 #4

    Stevecgz

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    Thanks George, I was able to solve the problem now.

    Steve
     
    Stevecgz, Sep 20, 2005
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