Question
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 $emf$ .
✓
Answer
Efficiency of an electric motor is maximum when the back $emf$ setup in the armature is half the value of the applied battery $emf$
Efficiency, $\eta \, = \,\frac{{{P_{out}}}}{{{P_{in}}}} = \frac{e}{E} = \frac{{{\text{Back emf}}}}{{{\text{Supply voltage}}}}$
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