A 3,5kW 240V single-phase motor draws 22,5A from the supply while operating at full load and efficiency of 90°. Calculate
a) The power factor at which the motor is operating
b) The phase angle at which the motor is operating
a) To calculate the power factor, we can use the formula:
Power factor = Real Power / Apparent Power
The real power can be calculated using the formula:
Real Power = Input Power x Efficiency
The input power can be calculated using the formula:
Input Power = Voltage x Current
Therefore, Real Power = 240V x 22.5A = 5400W
The apparent power can be calculated using the formula:
Apparent Power = Voltage x Current
Therefore, Apparent Power = 240V x 22.5A = 5400VA
Now we can calculate the power factor:
Power factor = Real Power / Apparent Power = 5400W / 5400VA = 1
Therefore, the power factor at which the motor is operating is 1.
b) To calculate the phase angle, we can use the formula:
Phase angle = arccos(Power factor)
Therefore, Phase angle = arccos(1) = 0°
Therefore, the phase angle at which the motor is operating is 0°.