A single-phase motor draws 0,75 kW from a 220V supply. If the motor is operating at unity power factor, calculate:
a) The current drawn by the motor
b) The phase angle at which the motor is operating
c) the reactive power of the motor
a) The power consumed by the motor is given as 0.75 kW. We can calculate the current drawn by using the formula:
Power (P) = Voltage (V) x Current (I) x Power Factor (PF)
Given that the power factor is unity, the formula simplifies to:
P = V x I
0.75 kW = 220 V x I
I = 0.75 kW / 220 V
I ≈ 0.0034 kA (kiloamperes)
Therefore, the current drawn by the motor is approximately 0.0034 kA.
b) Since the power factor is unity, the phase angle (θ) is 0 degrees.
Therefore, the motor is operating at a phase angle of 0 degrees.
c) The reactive power (Q) can be calculated using the formula:
Q = √(Apparent Power (S)^2 - Active Power (P)^2)
Given that the power factor is unity, the apparent power (S) is equal to the active power (P).
Q = √(0.75 kW)^2 - (0.75 kW)^2
Q = √(0.75)^2 - (0.75)^2
Q = √0.5625 - 0.5625
Q ≈ √0 - 0.5625
Q ≈ 0 - 0.5625
Therefore, the reactive power of the motor is approximately -0.5625 kVA (kilovolt-ampere) or kVAR (kilovolt-ampere reactive). The negative sign indicates that the reactive power is capacitive.