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
To solve this problem, we can use the following formulas:
a) Power factor (PF) = Real power (P) / Apparent power (S)
b) cos(θ) = PF
First, let's calculate the apparent power (S) using the formula:
S = V * I
where V is the voltage (240V) and I is the current (22.5A):
S = 240V * 22.5A
S = 5400 VA
a) The real power (P) can be calculated using the formula:
P = efficiency * apparent power
where the efficiency is given as 0.9:
P = 0.9 * 5400 VA
P = 4860 W
Now we can calculate the power factor (PF):
PF = P / S
PF = 4860 W / 5400 VA
PF ≈ 0.9
b) The phase angle (θ) can be calculated using the formula:
θ = cos^(-1)(PF)
θ = cos^(-1)(0.9)
θ ≈ 25.84°
Therefore, the motor is operating at a power factor of approximately 0.9 and a phase angle of approximately 25.84°.