$\"\"$

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(a)

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Calculate the RMS voltage of household current.

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The voltage of electricity is $\"\"$ , where $\"\"$ is the time in seconds.

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Voltmeters read the RMS (root-mean-square) voltage, which is the square root of the average value of $\"\"$ over one cycle.

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The function is $\"\"$ .

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Period of $\"\"$ is $\"\"$ .

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Average value of $\"\"$ is $\"\"$ .

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$\"\"$

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$\"\"$

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Let $\"\"$ , then $\"\"$ .

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The boundaries are $\"\"$ and $\"\"$ .

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$\"\"$

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$\"\"$

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$\"\"$

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Average rate of $\"\"$ is $\"\"$ .

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Therefore, RMS voltage of household current is $\"\"$ .

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$\"\"$

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(b)

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Find the corresponding amplitude needed for the voltage $\"\"$ .

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Many electric stoves require an RMS voltage of 220 V.

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If the amplitude of voltage is $\"\"$ with $\"\"$ , then the RMS voltage is $\"\"$ .

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RMS voltage : $\"\"$ .

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$\"\"$ .

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Therefore, the corresponding amplitude needed for the voltage $\"\"$ is $\"\"$ .

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$\"\"$

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(a) RMS voltage of household current is $\"\"$ .

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(b) The corresponding amplitude needed for the voltage $\"\"$ is $\"\"$ .