Question #14412

The plot shows 1/10 second of the voltage waveform of a 120V 60Hz AC (Alternating Current) power circuit, like that delivered to residences in the United States.
The actual voltage is 120⋅2√⋅cos(2π⋅60⋅t) Volts. If we apply this voltage across a resistor of resistance 110.0Ω the resistor will dissipate a time-varying power. What is the peak power (in Watts) dissipated by the resistor?
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What is the average power (in Watts) dissipated by the resistor? (Hint: you compute the average power by integrating the instantaneous power over one cycle of the waveform.)
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What would be the power (in Watts) dissipated by the resistor if the voltage was a constant value of 120V?
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If a time-varying, AC voltage dissipates the same power in a resistor as a constant voltage would dissipate, we say that the time-varying voltage has a root-mean-square (RMS) value that is equal to the constant voltage.

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