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A 220 V series motor takes a current 35 amp and runs at 500 rpm. Armature resistance =0.25W and series field resistance = 0.3W. If iron and friction losses amount to 600W. Whatis the armature torque
- a)134N
- b)138N
- c)154N
- d)156N
Correct answer is option 'A'. Can you explain this answer?
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A 220 V series motor takes a current 35 amp and runs at 500 rpm. Armat...
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A 220 V series motor takes a current 35 amp and runs at 500 rpm. Armat...
Given data:
- Voltage (V) = 220 V
- Current (I) = 35 A
- Speed (N) = 500 rpm
- Armature resistance (Ra) = 0.25 Ω
- Series field resistance (Rs) = 0.3 Ω
- Iron and friction losses = 600 W
Calculating back EMF (Eb):
The back electromotive force (EMF) in a series motor can be calculated using the formula:
Eb = V - (I * Ra)
Substituting the given values:
Eb = 220 V - (35 A * 0.25 Ω)
Eb = 220 V - 8.75 V
Eb = 211.25 V
Calculating torque (T):
The torque developed by a series motor can be calculated using the formula:
T = (Eb * I) / N
Substituting the given values:
T = (211.25 V * 35 A) / 500 rpm
T = 7393.75 VA / 500 rpm
T = 14.7875 Nm
Calculating armature torque (Ta):
The armature torque is the actual torque developed by the armature of the motor. It is given by:
Ta = T - Iron and friction losses
Substituting the given value for iron and friction losses:
Ta = 14.7875 Nm - 600 W
Since the units for torque and power are different, we need to convert the power into torque using the formula:
Power = Torque * Angular velocity (ω)
Given that the speed is in rpm, we need to convert it to rad/s:
ω = (2π * N) / 60
Substituting the given value for speed:
ω = (2π * 500 rpm) / 60
ω = 52.35988 rad/s
Now, we can calculate the torque equivalent of the iron and friction losses:
Iron and friction losses = Ta * ω
Substituting the given value for iron and friction losses:
600 W = Ta * 52.35988 rad/s
Solving for Ta:
Ta = 600 W / 52.35988 rad/s
Ta = 11.46819 Nm
Finally, substituting the value of Ta into the equation for armature torque:
Ta = 14.7875 Nm - 11.46819 Nm
Ta = 3.31931 Nm
Therefore, the armature torque is approximately 3.32 Nm.
- Voltage (V) = 220 V
- Current (I) = 35 A
- Speed (N) = 500 rpm
- Armature resistance (Ra) = 0.25 Ω
- Series field resistance (Rs) = 0.3 Ω
- Iron and friction losses = 600 W
Calculating back EMF (Eb):
The back electromotive force (EMF) in a series motor can be calculated using the formula:
Eb = V - (I * Ra)
Substituting the given values:
Eb = 220 V - (35 A * 0.25 Ω)
Eb = 220 V - 8.75 V
Eb = 211.25 V
Calculating torque (T):
The torque developed by a series motor can be calculated using the formula:
T = (Eb * I) / N
Substituting the given values:
T = (211.25 V * 35 A) / 500 rpm
T = 7393.75 VA / 500 rpm
T = 14.7875 Nm
Calculating armature torque (Ta):
The armature torque is the actual torque developed by the armature of the motor. It is given by:
Ta = T - Iron and friction losses
Substituting the given value for iron and friction losses:
Ta = 14.7875 Nm - 600 W
Since the units for torque and power are different, we need to convert the power into torque using the formula:
Power = Torque * Angular velocity (ω)
Given that the speed is in rpm, we need to convert it to rad/s:
ω = (2π * N) / 60
Substituting the given value for speed:
ω = (2π * 500 rpm) / 60
ω = 52.35988 rad/s
Now, we can calculate the torque equivalent of the iron and friction losses:
Iron and friction losses = Ta * ω
Substituting the given value for iron and friction losses:
600 W = Ta * 52.35988 rad/s
Solving for Ta:
Ta = 600 W / 52.35988 rad/s
Ta = 11.46819 Nm
Finally, substituting the value of Ta into the equation for armature torque:
Ta = 14.7875 Nm - 11.46819 Nm
Ta = 3.31931 Nm
Therefore, the armature torque is approximately 3.32 Nm.
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A 220 V series motor takes a current 35 amp and runs at 500 rpm. Armature resistance =0.25W and series field resistance = 0.3W. If iron and friction losses amount to 600W. Whatis the armature torquea)134Nb)138Nc)154Nd)156NCorrect answer is option 'A'. Can you explain this answer?
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