Answer MET Question 24

Question :  What is back emf? Derive the relation for the back emf and the supplied voltage in terms of armature resistance.

Answer: 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 emf is induced in the armature as in a generator. The induced emf 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 emf. This can be deduced by Lenz's law, which states that the direction of an induced emf is such as to oppose the change causing it, which is the applied voltage.  The magnitude of the back emf can be calculated by using the formula: $\displaystyle \small \mathrm{E_b = \frac{P\phi NZ}{60A}}$
where P = Number of poles
 phi = flux/pole, in wb
N = rotational speed of armature
Z = total number of armature conductors,
   = number of slots x number of conductors/ slot,
A = Number of parallel path
For lap wound motor A=P
and for wave wound motor A=2
The value of back emf is always less than the applied voltage.

The diagram above shows a simple connection of a d.c motor.
$\displaystyle \small \mathrm{V=E_b+I_aR_a}$
V = applied voltage
$\displaystyle \small \mathrm{E_b}$ = Back emf
$\displaystyle \small \mathrm{I_a}$ = Armature current
$\displaystyle \small \mathrm{R_a}$ = Armature resistance.