Electromagnetic torque 

The torque is given by the force on the armature winding multiplied by its radius. Force on a conductor in magnetic field B is: 

F=B.I.L

so, T=B.I.L.R

The torque opposes the mechanical rotation of the rotor and so the mechanical torque turning the generator must do work against the electromagnetic torque in order to generate the voltage (and current) supplied to the electrical load connected to the generator. Therefore energy conversion occurs from mechanical energy to electrical energy.The flux density B webers/m  can be expressed in terms of the flux per pole, φ,  to give a relation between the electromagnetic torque to be overcome and current produced.

T=C_m.Ø.I_a

C_m  =machine constant

The equivalent circuit representation of an electrical generator is:

The generator itself provides the source tosupply the field current I . Residualmagnetism will provide a small generatedcurrent at first that then builds up as thefield current grows, producing moregenerated current, etc. [NB leaving analternator open circuit will cause thevoltage to build up to the point wherediodes used to rectify the output voltagecan be damaged. Never operate an alternator without an electrical load connected. The output voltage is slightly less than the generated voltage due to the volt drop across the armature winding resistance when current flows. The arrangement of connecting the field winding in parallel with the armature is known as a shunt connected machine. The alternative is to connect the field winding in series with the armature, in which case it as known as a series connected machine.

Reversibility principle of electric machines

An electric machine can be operated as a generator or motor depending on the operation conditions. This is known as the reversibility principle of electric machines. For example, if the generator above is supplied from an electrical source, it will operate as a motor