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Household electricity is supplied in the form of alternating current that varies from 155 $\mathrm{V}$ to $-155 \mathrm{V}$ with a frequency of 60 cycles per second...

Question

Household electricity is supplied in the form of alternating current that varies from 155 $\mathrm{V}$ to $-155 \mathrm{V}$ with a frequency of 60 cycles per second $(\mathrm{Hz})$ . 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. $$\begin{array}{l}{\text { (a) Calculate the RMS voltage of household cu

Household electricity is supplied in the form of alternating current that varies from 155 $\mathrm{V}$ to $-155 \mathrm{V}$ with a frequency of 60 cycles per second $(\mathrm{Hz})$ . 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. $$\begin{array}{l}{\text { (a) Calculate the RMS voltage of household current. }} \\ {\text { (b) Many electric stoves require an RMS voltage of } 220 \mathrm{V} \text { . }} \\ {\text { Find the corresponding amplitude } A \text { needed for the voltage } E(t)=A \sin (120 \pi t)}\end{array}$$



Answers

Household electricity is supplied in the form of alternating current that varies from 155 $\mathrm{V}$ to $-155 \mathrm{V}$ with a frequency of 60 cycles per second $(\mathrm{Hz})$ . 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.

$$\begin{array}{l}{\text { (a) Calculate the RMS voltage of household current. }} \\ {\text { (b) Many electric stoves require an RMS voltage of } 220 \mathrm{V} \text { . }} \\ {\text { Find the corresponding amplitude } A \text { needed for the voltage } E(t)=A \sin (120 \pi t)}\end{array}$$


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