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JH

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 (Hz). 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 require an $RMS$ voltage of 220 V. Find the corresponding amplitude A neededfor the voltage $E(t) = A \sin (120 \pi t)$.

a) RMS Voltage $=\sqrt{\frac{155^{2}}{2}}=\frac{155}{\sqrt{2}}$b) Amplitude $(\mathrm{A})=220 \sqrt{2}$ Volts

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Samuel H.

University of Nottingham

Michael J.

Idaho State University

Boston College

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JH

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Samuel H.

University of Nottingham

Michael J.

Idaho State University

Boston College

Lectures

Join Bootcamp