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°.
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
1 answer
1 answer