This month we will complete our review of fundamentals by covering the basic concepts of alternating current (ac) circuits. With this material under our belts, we can then turn to practical applications.

## AC Potential

An "ac potential" is a voltage that regularly reverses its polarity over time. In electrical power systems, most ac voltages follow a simple, sinusoidal function of time between the peak values of polarity reversal (Figure 1). The sine wave is an inherent characteristic of ac generators, which produce electric potential through the rotation of a magnetic field (rotor) within a winding of multiple turns of wire (stator).The frequency (f) of such a waveform is the number of complete cycles contained within a 1-sec interval, with units of cycles/sec or Hertz (Hz). In North America the standard power system frequency is 60 Hz, while much of Europe uses 50 Hz.

The standard means of expressing the magnitude of an ac voltage is the root mean square (RMS) value, where VRMS = v(1 T? v2dt). For a pure sine wave without harmonics, the RMS value is about 70% of the peak value.

The RMS value is also known as the effective value or the equivalent heating value; the power dissipated in a resistor with an applied ac potential of 120 VRMS is equal to that dissipated in the same resistor with an applied dc potential of 120 V.

## Three-Phase Power

An important concept in ac power circuits is that of phase, describing the relationship in time between two ac waveforms.If two waveforms have their positive and negative peaks coincide in time, they are said to be in phase. If their peaks are shifted with respect to one another, we say they are out of phase and express the phase shift in degrees, with a full cycle being 360 degrees.

The common three-phase power systems we use are based on three source voltages shifted in phase by 120 degrees, as shown in Figure 2. These voltages are produced by placing three separate windings around the circumference of a generator so that they are affected by the rotating magnetic field 120 degrees apart.

A major advantage of this system is that by applying these voltages to three windings similarly placed around the circumference of an electric motor, the currents will create a rotating magnetic field in the motor, producing the torque required to turn the rotor.

## Power Factor

An ac voltage applied to a resistor results in a current that is in phase with the applied voltage. In-phase, or active, current results in power dissipation and produces energy conversion, or work.The current in an inductor follows (lags) the applied voltage by a quarter cycle, or 90 degrees of phase, while that in a capacitor leads the voltage by 90 degrees. These out-of-phase currents, called reactive currents, are associated with alternating energy storage and removal in these circuit elements and do not produce useful work. Actual circuits have a combination of circuit elements and thus draw a current that is somewhere between 90 degrees lagging and 90 degrees leading.

We express the degree to which the current in an ac circuit is in phase with the voltage by the term power factor (PF), defined as the cosine of the phase angle. If the current in a circuit lags the voltage by 37 degrees, the power factor is 0.8, or 80%. Since the cosine is positive on both sides of zero, the numerical value must be accompanied by an indication of leading or lagging. If this is omitted, lagging is assumed.

Power factor is also the ratio of active current to total current in an ac circuit, and it serves as an index of how efficiently we are using the capacity of the circuit. This makes the operating power factor of equipment (such as motors and variable-speed drives) an important specification item.