Voltage Calculations:

Equation (7-9) is a mathematical representation of the voltage related along with any particular orientation of a coil (inductor).

e = E_max   sinθ                                                (7-9)

where

e  = induced EMF

E_max     = maximum induced EMF

θ  = angle from reference (degrees or radians)

Example: What is the induced EMF in a coil generating a maximum EMF of 120 V whenever the angle from reference is 45°?

e = E_max  sinθ

e = 120 V (sin 45°)

e = 84.84 V

The maximum induced voltage could also be known as peak voltage E_p.  If (t) is the time in that the coil turns by the angle (θ), then the angular velocity (ω) of the coil is equal to θ /t and is expressed in units of radians/sec.  The above Equation is the mathematical representation of the angular velocity.

θ =ωt                                                   (7-10)

where

ω = denote angular velocity (radians/sec)

t = time to turn through the angle from reference (sec)

θ = angle from reference (radians)

By using substitution laws, a relationship among the voltage induced or the maximum induced voltage and the angular velocity could be expressed. Equation (7-11) is the mathematical representation of the relationship among the voltage induced and the maximum voltage and the angular velocity and is equivalent to the output of an AC Generator.

E = E_max   sin (ω t)                                                (7-11)

where

e = denotes induced EMF (volts)

E_max = maximum induced EMF (volts)

ω = angular velocity (radians/sec)

t = denotes time to turn by the angle from reference (sec)