A 3,5kW 240V single-phase motor draws 22,5A from the supply while operating at full load and an 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 need to find the apparent power (S) and the real power (P).
Apparent power (S) is given by:
S = V x I
S = 240V x 22.5A
S = 5400 VA
Real power (P) is given by:
P = S x power factor
P = 3.5kW x 0.9
P = 3.15 kW
To find the power factor, we can rearrange the formula and solve for it:
power factor = P / S
power factor = 3.15 kW / 5400 VA
power factor ≈ 0.583
The power factor at which the motor is operating is approximately 0.583.
b) The phase angle at which the motor is operating can be calculated using the power factor.
The power factor (pf) can be expressed in terms of the cosine of the phase angle (θ):
pf = cos(θ)
Rearranging the formula to solve for the phase angle:
θ = arccos(pf)
θ = arccos(0.583)
Using a calculator, the phase angle is approximately 54.53 degrees.
Therefore, the phase angle at which the motor is operating is approximately 54.53 degrees.