In torque-slip characteristics of an induction motor, at normal speeds close to synchronism the torque is:a)directly proportional to the slipb)not dependent on the slipc)maximumd)inversely proportional to the slip.Correct answer is option 'A'. Can you explain this answer?

Question

Answer

The torque in a three-phase induction motor is given by,

Observations:
1. At standstill,

Torque is directly proportional to the square of the supply voltage.
2. For the low values of slip, i.e. for the speeds close to the synchronous speed

i.e. the effective rotor circuit resistance is very large compared to the rotor reactance.

T ∝ s
Torque is directly proportional to slip. Thus, torque-slip characteristics are linear in the lower slip region.
3. For the high values of slip, i.e. for the speeds away from the synchronous speed

i.e. the effective rotor circuit resistance is very small compared to the rotor reactance.

T ∝ 1/s
Torque is inversely proportional to slip. Thus, torque-slip characteristics are rectangular hyperbola at higher slip region.

Answer

The torque in a three-phase induction motor is given by,

Observations:
1. At standstill,

Torque is directly proportional to the square of the supply voltage.
2. For the low values of slip, i.e. for the speeds close to the synchronous speed

i.e. the effective rotor circuit resistance is very large compared to the rotor reactance.

T ∝ s
Torque is directly proportional to slip. Thus, torque-slip characteristics are linear in the lower slip region.
3. For the high values of slip, i.e. for the speeds away from the synchronous speed

i.e. the effective rotor circuit resistance is very small compared to the rotor reactance.

T ∝ 1/s
Torque is inversely proportional to slip. Thus, torque-slip characteristics are rectangular hyperbola at higher slip region.

Answer

Torque-slip characteristics of an induction motor

The torque-slip characteristics of an induction motor represent the relationship between the torque produced by the motor and the slip, which is the difference between the synchronous speed and the actual speed of the motor.

Explanation of the answer
The correct answer to the given question is option 'A' - the torque is directly proportional to the slip at normal speeds close to synchronism.

Reasoning
To understand why torque is directly proportional to slip at normal speeds close to synchronism, let's consider the operating principles of an induction motor.

1. Slip
Slip is defined as the difference between the synchronous speed (Ns) and the actual speed of the rotor (N). It is denoted by the symbol 's' and is given by the formula:
s = (Ns - N) / Ns

2. Torque
The torque produced by an induction motor is directly proportional to the square of the rotor current and the rotor resistance. It is given by the formula:
T = K * I^2 * R2

3. Relationship between torque and slip
At normal speeds close to synchronism, the slip is small, which means that the rotor speed is very close to the synchronous speed. As a result, the difference between the synchronous speed and the actual speed is small, leading to a small value of slip.

When the slip is small, the torque produced by the motor is directly proportional to the slip. This is because a small slip indicates that the rotor is very close to the synchronous speed, and any deviation from synchronism will result in a torque that tries to bring the rotor back into synchronism.

Therefore, at normal speeds close to synchronism, the torque is directly proportional to the slip. As the slip increases, the torque decreases, and vice versa.

Conclusion
In the torque-slip characteristics of an induction motor, the torque is directly proportional to the slip at normal speeds close to synchronism. This relationship is due to the operating principles of an induction motor, where any deviation from synchronism results in a torque that tries to bring the rotor back into synchronism.

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