7.3. Back or Counter E.M.F.
Refer Fig. 52. In a D.C. motor when the armature rotates, the conductors on it cut the lines of force of magnetic field in which they revolve, so that an e.m.f is induced in the armature as in a generator. The induced e.m.f. acts in opposition to the current in the machine and, therefore, to the applied voltage, so that it is customary to refer to this voltage as the ‘back e.m.f:’ That this is so can be deduced by Lenz’s law, which states that the direction of an induced e.m.f. is such as to oppose the change causing it, which is, of course, the applied voltage.
The magnitude of the back or counter e.m.f. can be calculated by using formula for the induced e.m.f. in a generator, and it is important in the case of the motor, to appreciate that this is proportional to the product of the flux and the speed. Thus if Eb denotes the back e.m.f., the flux and N the speed, we may write,
Eb = k ɸ N
Fig. 52. Motoring operation.
The value of back e.m.f. (Eb) is always less than the applied voltage, although difference is small when the machine is running under normal conditions. It is the difference between these two quantities which actually drives current through the resistance of the armature circuit. If this resistance is represented by Ra, the back e.m.f. by Eb and the applied voltage by V, then we have
V = Eb + IaRa
where Ia is the current in the armature circuit.