Household electrical voltages are typically quoted as either 110 V, 115V, 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

Where T = the period of the wave form, Vm is the peak voltage, and w = the wave form frequency (f = 60 Hz in North America).

(a) Perform the indicated integration, and show that for a sinusoidal voltage.

(b) Compoute the peak voltages corresponding to the ms voltages of 110 , 115. and 120 V.

Vms= 6 S V cos (wt) di Vrms Vm 2