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 assertion and reason are ture and reason is the correct explanation of asseriton.
B. If both assertion and reason are true but reason is not the correct explanation of asseriton.
C. If assertion is true but reason is false
D. If both assertion and reason are false.

Answer

C

Explanation

(c ) Since, the efficiency of an electric motor is given by
`eta = ("outputpower")/("Inputpower")`
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 )`
To obtain maximum output power differenatiating Eq. (i) with respects 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 effieiency of motor will be maximum.