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Integration problem about household electricity

  • Thread starter Stevecgz
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  • #1
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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:

Answers and Replies

  • #2
George Jones
Staff Emeritus
Science Advisor
Gold Member
7,259
790
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
 
  • #3
George Jones
Staff Emeritus
Science Advisor
Gold Member
7,259
790
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
 
  • #4
68
0
Thanks George, I was able to solve the problem now.

Steve
 

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