A 60 hp, 3-phase motor absorbs 50 kW from a 600 V, 3-phase line. If the line cur

Question

A 60 hp, 3-phase motor absorbs 50 kW from a 600 V, 3-phase line. If the line current is 60 A, calculate the following: (a) The efficiency of the motor (b) The apparent power absorbed by the motor (c) The reactive power absorbed by the motor (d) The power factor of the motor

Assume the motor is connected in wyne and that each branch can be represented by a resistance R in series with an inductive reactance X. (a) Calculate the value of R and X. (b) What is the phase angle between the line current and the corresponding line to neutral voltage?

Explanation / Answer

Output power Pout = 60*746 = 44760 W
Active power absorbed P = 50 kW
a) Efficiency = Pout/P = 44.76/50 = 0.8952 = 89.52 %
b)the apparent power absorbed by the motor Pa= sqrt(3)*V*I = 62.354 kW
c)the reactive power absorbed by the motor Pr= sqrt(Pa^2 - P^2) = sqrt(62.354^2 - 50^2) = 37.26 kW
c) sqrt(3)*V*I*pf = P
Power factor pf = P/(sqrt(3)*V*I) = 0.80   

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