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Examoogle • User • info@examoogle.com • EE-2024-8821
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When the ratio of back E.MF to applied voltage is ___ than the mechanical power develop by the shunt generator is maximum?
1
5
2
3
5
Quick Summary: 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.
In a DC motor, the mechanical power developed is maximum when the ratio of back EMF (Eb) 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.
Pm=EbIa — Mechanical power developed
VEb=0.5 — Ratio for maximum power
The mechanical power developed (Pm) in a DC motor is given by Pm=Eb⋅Ia. Substituting Ia=RaV−Eb, we get Pm=Eb⋅RaV−Eb=RaV⋅Eb−Eb2. To find the maximum, we set the derivative dEbdPm=0, which yields V−2Eb=0, or VEb=0.5.
The maximum power condition assumes constant supply voltage V and armature resistance Ra.
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.
Useful in understanding power transfer limitations
Establishes a fundamental limit for electrical machine torque analysis
Motor efficiency drops to 50% at maximum power transfer
High currents lead to overheating and potential demagnetization
DC drive sizing
Electromechanical system performance optimization
The condition VEb=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.
B is correct — Mechanical power developed in a DC motor is maximum when the back EMF is exactly half of the applied terminal voltage.
Always remember that maximum power transfer in DC machines happens at 50% efficiency, which is a major constraint in practical motor design.