Question

If the load current and flux of a DC motor are held constant and voltage applied across its armature is increased by 5%, the speed of the motor will
a) Reduce by 5%
b) Increase by 5%
c) Depends on other factor
d) Remain unchanged

Answer 1

Hint: On application of the load to the DC motor the armature current decreases. As a result the speed of the motor also decreases. In the question it is given that the load current and the flux of DC are constant whereas the voltage across the armature is increased. Hence by knowing the relation of the speed of the motor in terms of the above mentioned parameters will enable us to determine the correct answer.
Formula used:
$E=\dfrac{NP\phi Z}{60A}$

Complete answer:
Let us say we have a DC motor connected to a battery of emf ‘E’. Let us say the speed of the motor is ‘n’ i.e. number of revolution per minute (rpm), the number of poles be P, number of parallel paths be A and the total number of conductors in the armature be Z. Than the relation between all the above parameters is given by,
$E=\dfrac{NP\phi Z}{60A}$
Arranging the above equation to get the expression for the speed of the motor we get,
$N=\dfrac{60AE}{PZ\phi }$
The parameters 60A, P, Z, are all constant as they depend on the internal design of the motor. If ‘k’ is the constant representing the above parameters, the above equation can be re-written as,
$N=\dfrac{E}{k\phi }$ where k is $k=\dfrac{PZ}{60A}$
If we observe the equation of the speed of the motor it is directly proportional to the applied emf and inversely proportional to the flux per pole. Since the flux is maintained constant and the emf of the applied voltage is increased by 5%, the above relation being a linear relation the speed of the motor will also increase by 5% of its initial value.

Therefore the correct answer of the above question is option b.

Note:
The armature of the motor is nothing but the coil of the motor. In case of a DC motor, the armature is attached to the split ring or a commutator to ensure the action of force on the coil to be in the same direction by reversing the current. Hence the motor rotates in only one direction.