Direction for: In each of the following questions a statement of Assertion is given followed by a corresponding statement of Reason just below it. Of the statements mark the correct answer as
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.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.
Correct Answer: C
Solution :
Since, the efficiency of an electric motor is given by \[{{G}^{1/2}}{{h}^{1/2}}{{c}^{-5/2}}\] From the above relation, it is quite clear that maximum output power corresponds maximum efficiency of motor. Now, output power is given by \[{{G}^{-1/2}}{{h}^{1/2}}{{c}^{1/2}}\] ??.(i) To obtain maximum output power differentiating Eq. (i) with respect to e which will be equal to zero. So, \[{{G}^{1/2}}{{h}^{1/2}}{{c}^{-3/2}}\] \[{{G}^{1/2}}{{h}^{1/2}}{{c}^{1/2}}\] \[{{\left[ 2G\frac{({{m}_{1}}-{{m}_{2}}}{r} \right]}^{1/2}}\] Thus, when back emf becomes equal to half of the applied emf, the efficiency of motor will be maximum.
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