Household electrical voltages are typically quoted as either 110 V, 115 V, or 120 V
Chapter 10, Problem 9(choose chapter or problem)
Household electrical voltages are typically quoted as either 110 V, 115 V, or 120 V. However, these values do not represent the peak ac voltage. Rather, they represent what is known as the root mean square of the voltage, defined as
\(V_{\mathrm{rms}}=\sqrt{\frac{1}{T} \int_{0}^{T} V_{m}^{2} \cos ^{2}(\omega t) d t}\)
where T = the period of the waveform, \(V_m\) is the peak voltage, and \(\omega =\) the waveform frequency ( f = 60 Hz in North America).
(a) Perform the indicated integration, and show that for a sinusoidal voltage,
\(V_{\mathrm{rms}}=\frac{V_{m}}{\sqrt{2}}\)
(b) Compute the peak voltages corresponding to the rms voltages of 110, 115, and 120 V.
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