Frequency Calculations:

The frequency of an alternating voltage or current could be associated directly to the angular velocity of a rotating coil.  Units of angular velocity are radians per second, and 2Π radians are a full revolution.  A radian is an angle which subtends an arc equal to the radius of a circle.  A single radian equals 57.3 degrees.  One cycle of the sine wave is produced when the coil rotates 2Π radians. Equation (7-13) is the mathematical relationship among frequency (f) and the angular velocity ( ω ) in an AC circuit.

ω = 2Πf                                                                                   (7-13)

where

ω = angular velocity (radians/sec)

f  = frequency (HZ)

Example:    The frequency of a 120 V AC circuit is 60 Hz.  Find out the following:

1. Angular velocity     

2. Angle from reference at 1 msec

3. Induced EMF at that point

Solution:

 1. ω =   2Πf

=   2 (3.14) (60 Hz)

=   376.8 radians/sec

2. θ = ωt

= (376.8 radian/sec) (.001 sec)

= 0.3768 radians

3. e =   E_max  sinθ

= (120 V) (sin 0.3768 radians)

= (120 V) (0.3679)

= 44.15 V