Assertion : An electric motor will have maximum efficiency when back emf becomes equal to half of applied emf.
Reason : Efficiency of electric motor depends only on magnitude of back emf.

Options

A. If both the assertion and reason are true and reason is a true explantion of the assertion.
B. If both the assertion and reason are true but the reason is not true the correct explantion of the assertion.
C. If the assertion is true but reason false
D. If both the assertion and reason are false.

Answer

C

Explanation

Since the effective of an electric motor is given by
`eta=("output power")/("input power")`
From the above relation, it is quite clear that maximum output power corresponds maximum efficiency of motor.
Now, output power is given by
`eI=(e(E-e))/R.....(i)`
To obtain maximum output power differentiating Eq. (i) with repect to `e` which will be equal to zero.
so, `d/(de)[(e(E-e))/R]=0 implies e=E/2`
Thus, when back emf becomes equal to half of the applied emf, the efficiency of motor will be maximum.