# Electric Motors And Generators/Single-phase

## Single Phase Alternating Current

### From a wire in a magnetic field to the Mains/line power source

Basically an electric voltage is generated in a wire if either that wire is in a changing magnetic field, or if the wire is moved into or out of a magnetic field. Single phase Alternating voltage (and Alternating Current if there is something connected to that wire or coil) is produced when a magnet, or magnet equivalent, is rotated inside a coil of wire. The more turns of wire there are in that coil, the higher the voltage, and the faster the rotation, the higher the frequency. If a graph would be drawn showing the relation of the voltage at the terminals of the coil with time, then that graph would be of sinusoidal shape, alternating between positive (+Ve) and negative (−Ve) in a complete rotation. If the coil would be rotated at a speed of 3000 revolutions per minute, then there would be 3000/60=50 cycles per second (= 50 Hz), the unit's name being Hertz (Hz), and if the coil would be rotated at 3600 revolutions per minute then the voltage would change at a frequency of 60 Hz. The usual AC (mains or line) frequency is 50 or 60 Hz, depending on the country concerned.

The electrical power available in North American homes is single phase 60 Hertz 120 volts. AC current's advantage over DC current is the efficient transmission over long distances using step-up and step-down transformers.

• Note that 3-phase transformers are, in fact, 3 single-phase transformers whose voltages are 120 degrees displaced from the other two, and that any terminal of a 3-phase transformer versus the neutral terminal (shown as N below) has a single phase voltage. A building's load could, for example, be divided into three separate single-phase loads, more or less equal to one another; these loads would be supplied from a three-phase transformer, all three voltages being versus the neutral terminal; that terminal is usually connected to ground/earth.

120 volts is the root mean square (${\displaystyle V_{rms}}$) of the maximum voltage (${\displaystyle V_{max}}$) .

${\displaystyle V_{rms}={\frac {V_{max}}{\sqrt {2}}}}$

${\displaystyle V_{max}=V_{rms}\cdot {\sqrt {2}}}$

${\displaystyle V_{max}=120\ volts\cdot 1.414=170\ volts}$