Question

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

• A. If both Assertion and Reason are true and the Reason is the correct explanation of the Assertion.
• B. If both Assertion and Reason are true but the Reason is not the correct explanation of the Assertion.
• C. If Assertion is true but Reason is false.
• D. If both Assertion and Reason are false.

Answer 1

Answer: (C)

If Assertion is true but Reason is false.

Answer 2

Since, the efficiency of an electric motor is given by $\eta=\frac{\text { output power }}{\text { input power }}$ From the above relation, it is quite clear that maximum output power corresponds maximum efficiency of motor. Now, output power is given by $=e I=\frac{e(E-e)}{R}$ ... (i) To obtain maximum output power differentiating E (i) with respect to $e$ which will be equal to zero. So, $\frac{d}{d e}\left[\frac{e(E-e)}{R}\right]=0$ $\Rightarrow e=\frac{E}{2}$ Thus, when back emf becomes equal to half of the applied emf, the efficiency of motor will be maximum.