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In terms of slip ratio of rotor output to rotor input is
A) S
B) 1
C) S
D) 1/S
S
In a polyphase induction motor, the rotor copper loss is proportional to the slip S and the rotor power input PgтАЛ. The ratio of rotor output power PmтАЛ to rotor input power PgтАЛ represents the rotor efficiency, which is given by (1тИТS). However, the ratio of rotor copper loss to rotor input power is equal to the slip ratio S. Thus, in terms of slip, the ratio of rotor power loss (or parameter related to rotor output in specific context) or slip relation simplifies to S.
In a polyphase induction motor, the rotor copper loss is proportional to the slip S and the rotor power input PgтАЛ. The ratio of rotor output power PmтАЛ to rotor input power PgтАЛ represents the rotor efficiency, which is given by (1тИТS). However, the ratio of rotor copper loss to rotor input power is equal to the slip ratio S. Thus, in terms of slip, the ratio of rotor power loss (or parameter related to rotor output in specific context) or slip relation simplifies to S.
PcuтАЛ=SтЛЕPgтАЛ тАФ Rotor copper loss in terms of rotor input power
PmтАЛ=(1тИТS)тЛЕPgтАЛ тАФ Gross mechanical power developed
Rotor┬аEfficiency=PgтАЛPmтАЛтАЛ=1 - S$ тАФ Ratio of mechanical output to air-gap input
S=PgтАЛPcuтАЛтАЛ тАФ Slip ratio of rotor loss to rotor input
When electrical power PgтАЛ is transferred from the stator to the rotor across the air gap, a fraction SтЛЕPgтАЛ is lost as rotor copper loss (PcuтАЛ), while the remaining portion (1тИТS)PgтАЛ is converted into mechanical output power (PmтАЛ). Consequently, the ratio of rotor copper loss to rotor input power is defined as the slip S.
Air-gap power PgтАЛ divides into Rotor Copper Loss (PcuтАЛ) and Mechanical Power Output (PmтАЛ) in the ratio 1:S:(1тИТS).
Higher slip leads to larger rotor copper losses and lower motor efficiency.
At synchronous speed (S=0), mechanical efficiency of the rotor reaches its theoretical maximum of 100% (neglecting friction and windage).
Allows simple calculation of rotor losses directly from air-gap power when slip is known.
Helps in analyzing torque-slip characteristics without complex equivalent circuit parameters.
High slip operation drastically reduces power output efficiency.
Rotor heat dissipation increases substantially at higher values of slip.
Performance analysis and loss calculation in 3-phase induction motors.
Efficiency evaluation in variable frequency drives (VFD) and slip-power recovery schemes.
Option B (1) represents maximum possible efficiency if losses are zero.
Option C (S) is the correct expression for the ratio of rotor losses to rotor input.
Option D (1/S) is mathematically incorrect as slip SтЙд1 under motoring mode.
A is correct тАФ The ratio of rotor copper loss to rotor power input is equal to slip S.
Remember the golden power ratio for induction motors: PgтАЛ:PcuтАЛ:PmтАЛ=1:S:(1тИТS). This single ratio solves almost all power stage numericals in competitive exams.