# Integration problem about household electricity

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:

$$E(t) = 155\sin(120\pi t)$$

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.

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

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

Steve

Last edited:

George Jones
Staff Emeritus
Gold Member
Use an integral to calculate to calculate the average

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

where $T$ 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 $E$, then take the average, then take the square root.

Regards,
George

George Jones
Staff Emeritus
Gold Member
Use an integral to calculate to calculate the average

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

where $T$ 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 $E$, then take the average, then take the square root.

Regards,
George

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

Steve