hi guys, ive just joined the froum so helpfully you dont mind helping me. im totally lost with this question

a 3.3kw single-phase induction motor. The power factor is 0.8 lagging

Determine:

A)Current drawn from the 230V supply.
B)The output power if the overall motor efficiency is 85%
C)The active and reactive components of the input current.
D) The apparent power and reactive power consumed.

 

hi guys, ive just joined the froum so helpfully you dont mind helping me. im totally lost with this question

a 3.3kw single-phase induction motor. The power factor is 0.8 lagging

Determine:

A)Current drawn from the 230V supply.
B)The output power if the overall motor efficiency is 85%
C)The active and reactive components of the input current.
D) The apparent power and reactive power consumed.

A) current drawn =power/voltage=3300/230=14.35 amps

B) input power is Vrms*Irms*cosφ , where cosφ is the power factor=0.8
thus input power Pin=230*14.35*0.8=2640.4 watts
the efficiency is 85% thus the motor outputs 85% of its input power
so output power Pout=Pin*85%=2640.4*85/100=2244.34 watts

C) i am not sure what do you want

D) apparent power S=Vrms*Irms=230*14.35=3300 VA
reactive power Q=Vrms*Irms*sinφ

φ=arccos(0.8)=36.86 degrees

therefore Q=230*14.35*sin(36.86)=1979.84 VAR

 

thats great mike. very much apreciated. just ne lastquestion. where abouts did the 36.86 degress come from?

 

thats great mike. very much apreciated. just ne lastquestion. where abouts did the 36.86 degress come from?

power factor=cos(φ)=0.8

thus φ=arccos(0.8)=36.86