The frequency of an alternating voltage or current can be related directly to the angular velocity of a rotating coil. The units of angular velocity are radians per second, and 2 radians is a full revolution. A radian is an angle that subtends an arc equal to the radius of a circle. One radian equals 57.3 degrees. One cycle of the sine wave is generated when the coil rotates 2 radians. Equation (7-13) is the mathematical relationship between frequency (f) and the angular velocity ( ) in an AC circuit.

Example 1: The frequency of a 120 V AC circuit is 60 Hz. Find the following:

1. Angular velocity
2. Angle from reference at 1 msec
3. Induced EMF at that point



  • AC generation analysis is summarized below.
  • Voltage, Current, and Frequency Summary
  • The following terms relate to the AC cycle: radians/second, the velocity the loop turns; hertz, the number of cycles in one second; period, the time to complete one cycle.
  • Effective value of AC equals effective value of DC.
  • Root mean square (RMS) values equate AC to DC equivalents:

Phase angle is used to compare two wave forms. It references the start, or zero point, of each wave. It compares differences by degrees of rotation. Wave forms with the same start point are "in-phase" while wave forms "out-of-phase" either lead or lag.