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A 230 V,50 Hz,4-pole,single-phase induction motor is rotating (running) clockwise (forward) direction at a speed of 1425 rpm. If the rotor resistance at standstill is7.8Ω then the effective rotor resistance in the backward branch of the equivalent circuit will be.
- a)2.0Ω
- b)4.0Ω
- c)78Ω
- d)156Ω
Correct answer is option 'A'. Can you explain this answer?
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Most Upvoted Answer
A 230 V,50 Hz,4-pole,single-phase induction motor is rotating (runnin...
To determine the effective rotor resistance in the backward branch of the equivalent circuit, we need to consider the slip of the motor and the concept of rotor resistance.
1. Slip of the Motor:
The slip of an induction motor is defined as the difference between the synchronous speed and the actual speed divided by the synchronous speed. It is given by the formula:
Slip = (Ns - N) / Ns
Where,
Ns = synchronous speed (in RPM)
N = actual speed (in RPM)
In this case, the synchronous speed of the motor can be calculated using the formula:
Ns = (120 * f) / P
Where,
f = frequency of the power supply (in Hz)
P = number of poles
Given:
f = 50 Hz
P = 4
Substituting the values, we get:
Ns = (120 * 50) / 4
Ns = 1500 RPM
The actual speed of the motor is given as 1425 RPM. Therefore, the slip can be calculated as:
Slip = (1500 - 1425) / 1500
Slip = 0.05
2. Rotor Resistance:
The rotor resistance is given as 7.8Ω at standstill. However, the rotor resistance changes when the motor is running due to the skin effect and the influence of the rotor current on the rotor resistance. In this case, we need to determine the effective rotor resistance in the backward branch of the equivalent circuit.
The effective rotor resistance in the backward branch can be calculated using the formula:
R2' = R2 / (1 - s)
Where,
R2' = effective rotor resistance in the backward branch
R2 = rotor resistance at standstill
s = slip
Given:
R2 = 7.8Ω
s = 0.05
Substituting the values, we get:
R2' = 7.8 / (1 - 0.05)
R2' = 7.8 / 0.95
R2' ≈ 8.21Ω
Therefore, the effective rotor resistance in the backward branch of the equivalent circuit is approximately 8.21Ω.
However, none of the provided answer options match this value. Option 'A' with a value of 2.0Ω is incorrect.
1. Slip of the Motor:
The slip of an induction motor is defined as the difference between the synchronous speed and the actual speed divided by the synchronous speed. It is given by the formula:
Slip = (Ns - N) / Ns
Where,
Ns = synchronous speed (in RPM)
N = actual speed (in RPM)
In this case, the synchronous speed of the motor can be calculated using the formula:
Ns = (120 * f) / P
Where,
f = frequency of the power supply (in Hz)
P = number of poles
Given:
f = 50 Hz
P = 4
Substituting the values, we get:
Ns = (120 * 50) / 4
Ns = 1500 RPM
The actual speed of the motor is given as 1425 RPM. Therefore, the slip can be calculated as:
Slip = (1500 - 1425) / 1500
Slip = 0.05
2. Rotor Resistance:
The rotor resistance is given as 7.8Ω at standstill. However, the rotor resistance changes when the motor is running due to the skin effect and the influence of the rotor current on the rotor resistance. In this case, we need to determine the effective rotor resistance in the backward branch of the equivalent circuit.
The effective rotor resistance in the backward branch can be calculated using the formula:
R2' = R2 / (1 - s)
Where,
R2' = effective rotor resistance in the backward branch
R2 = rotor resistance at standstill
s = slip
Given:
R2 = 7.8Ω
s = 0.05
Substituting the values, we get:
R2' = 7.8 / (1 - 0.05)
R2' = 7.8 / 0.95
R2' ≈ 8.21Ω
Therefore, the effective rotor resistance in the backward branch of the equivalent circuit is approximately 8.21Ω.
However, none of the provided answer options match this value. Option 'A' with a value of 2.0Ω is incorrect.
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Community Answer
A 230 V,50 Hz,4-pole,single-phase induction motor is rotating (runnin...
Given
Frequency = 50 Hz
Poles = 4
Speed = 1425 rpm
Rotor resistance r2 = 7.8Ω
Slip due to forward field, sf = (1500 - 1425)/1500 = 75/1500 = 0.05
Rotor resistance due to backward field 
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A 230 V,50 Hz,4-pole,single-phase induction motor is rotating (running) clockwise (forward) direction at a speed of 1425 rpm. If the rotor resistance at standstill is7.8Ω then the effective rotor resistance in the backward branch of the equivalent circuit will be.a)2.0Ωb)4.0Ωc)78Ωd)156ΩCorrect answer is option 'A'. Can you explain this answer?
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