Generators The generalized equation for a generator is Motion + Magnetism → Electricity When a coil is rotated within a permanent external magnetic field, the changing flux lines generate a voltage within the coil. Since the coil has resistance, this induced emf will result in an induced electric current. The equation for the alternating voltage produced by the rotating coil is
v_{instantaneous} = V_{o}sin(2πf)t
where V_{o} is the coil's maximum emf which equals NBA(2πf) and the frequency is in rev/sec [hz]. This equation can also be expressed as
v_{instantaneous} = V_{o}sin(ωt)
where ω is the coil's angular velocity,
ω = 2πf.
Transformers
The Law of Transformers states
N_{s}/N_{p} = ε_{s}/ε_{p}
N_{p} and N_{s} are the number of loops in the primary and secondary coils. ε_{p} and ε_{s} are the emfs in the primary and secondary. A transformer only works when the number of flux lines through the iron core of the transformer keeps changing  therefore, the primary must be connected to an alternating source. Transformers will not operate in a DC circuit. Any change in flux in the primary is communicated to the secondary through the iron core.
The power utilized on both coils is the same since energy is conserved. Therefore, ε_{p}I_{p} = ε_{s}I_{s}, which explains how electricity is transferred by the power companies. High voltages will have smaller currents and less energy loss to Joule heating. Voltages are stepped down for use in buildings at transformers. When N_{s} < N_{p}, the transformer is a "step down" transformer since the induced AC voltage of the secondary will be less than the voltage across the primary.
