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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...
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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Community 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 understand the concept of slip and the equivalent circuit of an induction motor.
1. Slip:
The slip of an induction motor is defined as the difference between synchronous speed and rotor speed, divided by synchronous speed. It is denoted by 's' and is given by the formula:
s = (Ns - Nr) / Ns
where Ns is the synchronous speed and Nr is the rotor speed.
2. Synchronous Speed:
The synchronous speed of an induction motor is given by the formula:
Ns = 120 * f / P
where f is the supply frequency (50 Hz) and P is the number of poles (4 in this case).
3. Equivalent Circuit:
The equivalent circuit of an induction motor consists of the stator and rotor components. The rotor components include rotor resistance, rotor reactance, and rotor leakage reactance.
Now, let's solve the problem step by step:
Given data:
Supply voltage (V) = 230 V
Supply frequency (f) = 50 Hz
Number of poles (P) = 4
Rotor resistance at standstill (Rr) = 7.8 Ω
Rotor speed (Nr) = 1425 rpm
Step 1: Calculate the synchronous speed (Ns):
Ns = 120 * f / P
= 120 * 50 / 4
= 1500 rpm
Step 2: Calculate the slip (s):
s = (Ns - Nr) / Ns
= (1500 - 1425) / 1500
= 0.05
Step 3: Calculate the rotor resistance in the backward branch (Rr_eff):
Rr_eff = Rr / s
= 7.8 / 0.05
= 156 Ω
Therefore, the effective rotor resistance in the backward branch of the equivalent circuit is 156 Ω. The correct answer is option 'D'.
Note: The answer provided in the question as option 'A' (2.0 Ω) seems to be incorrect based on the given data.
1. Slip:
The slip of an induction motor is defined as the difference between synchronous speed and rotor speed, divided by synchronous speed. It is denoted by 's' and is given by the formula:
s = (Ns - Nr) / Ns
where Ns is the synchronous speed and Nr is the rotor speed.
2. Synchronous Speed:
The synchronous speed of an induction motor is given by the formula:
Ns = 120 * f / P
where f is the supply frequency (50 Hz) and P is the number of poles (4 in this case).
3. Equivalent Circuit:
The equivalent circuit of an induction motor consists of the stator and rotor components. The rotor components include rotor resistance, rotor reactance, and rotor leakage reactance.
Now, let's solve the problem step by step:
Given data:
Supply voltage (V) = 230 V
Supply frequency (f) = 50 Hz
Number of poles (P) = 4
Rotor resistance at standstill (Rr) = 7.8 Ω
Rotor speed (Nr) = 1425 rpm
Step 1: Calculate the synchronous speed (Ns):
Ns = 120 * f / P
= 120 * 50 / 4
= 1500 rpm
Step 2: Calculate the slip (s):
s = (Ns - Nr) / Ns
= (1500 - 1425) / 1500
= 0.05
Step 3: Calculate the rotor resistance in the backward branch (Rr_eff):
Rr_eff = Rr / s
= 7.8 / 0.05
= 156 Ω
Therefore, the effective rotor resistance in the backward branch of the equivalent circuit is 156 Ω. The correct answer is option 'D'.
Note: The answer provided in the question as option 'A' (2.0 Ω) seems to be incorrect based on the given data.
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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?
Question Description
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