Assertion : An electric motor will have maxim | vedclass

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(C) The efficiency $\eta$ of an electric motor is given by $\eta = \frac{P_{out}}{P_{in}} = \frac{e \cdot I}{E \cdot I} = \frac{e}{E}$, where $e$ is t

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If the Assertion is correct but Reason is incorrect.

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(C) The efficiency $\eta$ of an electric motor is given by $\eta = \frac{P_{out}}{P_{in}} = \frac{e \cdot I}{E \cdot I} = \frac{e}{E}$, where $e$ is the back $emf$ and $E$ is the applied $emf$.The current in the motor is $I = \frac{E - e}{R}$. The mechanical power output is $P_{out} = e \cdot I = e \left( \frac{E - e}{R} \right) = \frac{eE - e^2}{R}$.To maximize $P_{out}$, we differentiate with respect to $e$: $\frac{dP_{out}}{de} = \frac{E - 2e}{R} = 0$, which gives $e = \frac{E}{2}$. Thus, the assertion is correct.The efficiency depends on both the back $emf$ and the applied $emf$, not just the magnitude of the back $emf$. Therefore, the reason is incorrect.

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 $emf$.

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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 $emf$.