AC GENERATION ANALYSISBasic AC TheoryPhase difference is also used to compare two different currents or a current and a voltage. If thephase difference between two currents, two voltages, or a voltage and a current is zero degrees,they are said to be "in-phase." If the phase difference is an amount other than zero, they are saidto be "out-of-phase."VoltageCalculationsEquation (7-9) is a mathematical representation of the voltage associated with any particularorientation of a coil (inductor).(7-9)eE_{max} sinqwheree = induced EMFE_{max}= maximum induced EMFq= angle from reference (degrees or radians)Example 1: What is the induced EMF in a coil producing a maximum EMF of 120 V whenthe angle from reference is 45°?e = E_{max} sin qe = 120 V (sin 45°)e = 84.84 VThe maximum induced voltage can also be called peak voltage E_{p}. If (t) is the time in which thecoil turns through the angle (q), then the angular velocity (w) of the coil is equal to q/t and isexpressed in units of radians/sec. Equation (7-10) is the mathematical representation of theangular velocity.(7-10)qwtwherew = angular velocity (radians/sec)t = time to turn through the angle from reference (sec)q = angle from reference (radians)Using substitution laws, a relationship between the voltage induced, the maximum inducedvoltage, and the angular velocity can be expressed. Equation (7-11) is the mathematicalrepresentation of the relationship between the voltage induced, the maximum voltage, and theangular velocity, and is equal to the output of an AC Generator.(7-11)eE_{max} sin(wt)ES-07 Page 8 Rev. 0

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