Single-phase alternator.

A model of a simple single-phase alternator is easy to construct based on the same principle. A geometric configuration of such a device is shown in Fig. 69a. Wires wrapped around a rotor or armature rotating about the z axis are carried through a gap of substantially constant x-directed flux density B. The component of the conductor velocity perpendicular to the flux is

where r is the radius of the armature and is its angular velocity. It is this component which must be used in (94) for the voltage equation

where is the effective length of all conductors cutting the flux lines with an average density value B.

Wires may be wound many times around the armature, and the total voltage generated is the sum of all the voltages generated by each wrap. Note that voltage induced on one side of the rotor adds to that on the other because although the direction of flux cutting is opposite on two ends of the rotor diameter, the direction of current flow is also opposite on the two ends. The electric circuit can be completed with clip rings as shown.

If current starts to flow through the rotor winding, a force given by (93) will act on it giving rise to a torque opposing the rotation. The magnitude of the external torque required to hold the rotor in equilibrium will be

Figure 69: Single-phase ac rotational transducer.

This together indicates, that the alternator can be modeled by a pure transformer with the variable ratio

as shown in Fig. 69b. Pole C represents the rotational motion of the rotor.

Real alternators have more complicated configurations than the one shown schematically in Fig. 69a an may have sets of windings to generate three-phase power, but the basic modeling idea based on an energy-transfer transformer still applies.