When the ratio of back E.MF to applied voltage is ___ than the mechanical power develop by the shunt generator is maximum?
A
1
B
0.5
C
2
D
3

Question

When the ratio of back E.MF to applied voltage is ___ than the mechanical power develop by the shunt generator is maximum?

Examoogle · Accepted Answer

0.5

Explanation: In a DC motor, the mechanical power developed is maximum when the ratio of back EMF ($E_b$) to applied voltage ($V$) is 0.5. This condition corresponds to the point where the current drawn is half of the stall current (short circuit current), effectively delivering maximum power to the load.

Working Principle: The mechanical power developed ($P_m$) in a DC motor is given by $P_m = E_b \cdot I_a$. Substituting $I_a = \frac{V - E_b}{R_a}$, we get $P_m = E_b \cdot \frac{V - E_b}{R_a} = \frac{V \cdot E_b - E_b^2}{R_a}$. To find the maximum, we set the derivative $\frac{dP_m}{dE_b} = 0$, which yields $V - 2E_b = 0$, or $\frac{E_b}{V} = 0.5$.

Key Formulas: $P_m = E_b I_a$ — Mechanical power developed; $\frac{E_b}{V} = 0.5$ — Ratio for maximum power

Key Points: The maximum power condition assumes constant supply voltage $V$ and armature resistance $R_a$.; At maximum power, the efficiency of the DC motor is typically 50% as half the power is lost in the armature resistance.; This condition is rarely used in continuous operation due to high current and heat dissipation limits.

Advantages: Useful in understanding power transfer limitations; Establishes a fundamental limit for electrical machine torque analysis

Disadvantages: Motor efficiency drops to 50% at maximum power transfer; High currents lead to overheating and potential demagnetization

Applications: DC drive sizing; Electromechanical system performance optimization

Additional Info: The condition $\frac{E_b}{V} = 0.5$ is often termed the 'Maximum Power Transfer Theorem' application in electrical machines.. Option B is correct because the differentiation of the power equation with respect to EMF leads to 0.5.

Answer: B is correct — Mechanical power developed in a DC motor is maximum when the back EMF is exactly half of the applied terminal voltage.

Exam Tip: Always remember that maximum power transfer in DC machines happens at 50% efficiency, which is a major constraint in practical motor design.

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