# When the speed of the DC motor is Increases its Armature current

When the speed of the DC motor is Increases its Armature current

#### SOLUTION

D.C. machines are generally much more adaptable to adjustable speed service. The ready availability of D.C. motors to adjustment of their operating speed over wide ranges and by a variety of methods is one of the important reasons for the strong competitive position of D. C. machinery in modern industrial applications.

### Voltage Equation of DC Motor

The voltage equation of the DC Motor is given as

V = Eb + IaRa

The voltage V applied across the motor armature has to
(i) overcome the back e.m.f. Eb and
(ii) supply the armature ohmic drop IaRa

The above equation can also be written as

Eb = V − IaRa

### Back EMF of DC Motor

When the armature of a d.c. the motor rotates under the influence of the driving torque, the armature conductors move through the magnetic field and hence e.m.f. is induced in them as in a generator. The induced e.m.f. acts in opposite direction to the applied voltage  V (Lenz’s law) and is known as back or counter e.m.f. Eb.

${E_b} = \dfrac{{P\Phi ZN}}{{60A}}$

Where

P – Number of poles of the machine

ϕ – Flux per pole in Weber.

Z – Total number of armature conductors.

N – Speed of armature in revolution per minute (r.p.m).

A – Number of parallel paths in the armature winding.

From the above equation, it is clear that the EMF of DC Motor is Directly proportional to the Number of poles of the machine (P), Flux per pole in Weber (ϕ), Total number of armature conductors(Z), and  Speed of armature (N)

From the voltage equation and Back EMF equation, we can conclude that

$\begin{array}{l}\dfrac{{P\Phi ZN}}{{60A}} = V – {\rm{ }}{I_a}{R_a}\\\\N = \dfrac{{V – {\rm{ }}{I_a}{R_a}}}{\Phi } \times \left( {\dfrac{{60A}}{{PZ}}} \right)r.p.m\\\\{E_b} = V – {\rm{ }}{I_a}{R_a}\\\\\therefore N = K\dfrac{{{E_b}}}{\Phi }\end{array}$

From the above equation it is clear that by increasing the speed of DC motor the back EMF increased but the armature current decrease.

Scroll to Top