motor efficiency and power factor

T

teeg123

Member
Location
Maine
Occupation
Journeyman Electrician
here is the question
What is the efficiency and power factor of a one horsepower, single phase, 208-volt motor?
36.80%
38.90%
40.70%
80.00%

formula for efficiency is n= (output power/ input power) *100
formula for power factor (PF)= active power(P) / apparent power (S)
because I got this wrong, I know the correct answer, but I just can't figure how they got it?
apparent power formula for single phase is S=V*I, S=208*8.8=1830.4
active power formula P=V×I×cosϕ P=208*8.8*cosϕ. this is where I get lost. I think I need to know power factor to get efficiency ?

thanks folks
 
Induction motor efficiency is dealing with what is happening inside that motor when running at nameplate load. Power factor is more about how the facility's electrical infrastructure handles the lagging reactive current that the motor causes.

You can have crappy power factor and still have high effieency. Like with overbuild of the conductors and transformer secondaries. Or with something as easy as a capacitor across the line.

So motor efficiency as stated on nameplates is concerned with all the losses ending at the peckerhead.

Power factor is your problem to handle and it all depends on the specifics of how you design your circuit

teeg123 said:
think I need to know power factor to get efficiency
Click to expand...
 
it would appear that the question has some missing information that is needed to correctly answer it. the answer they have is 40.70%
this was on a practice test, I can't see them putting a question like this on the actual state exam.
 
teeg123 said:
the answer they have is 40.70%
Click to expand...
You can get this answer by taking the NEC Table 430.248 full load current for a 1 HP 208V motor of 8.8A, and multiply with voltage to get 208 * 8.8 = 1830W. That would be input apparent power. Then 1 HP = 745.7W. The ratio is 745.7 / 1830 = 40.7%.

However, I would not call this effiency. I guess you could call it NEC worst-case apparent efficiency, as it is using apparent input power instead of real input power, and the NEC design full load current should be a worst case motor effiency that you wire for; actual motors you install should have a full load current that is no more than 8.8A. If the power factor were 100%, apparent power would equal real power, and it would be worst-case efficiency. But I understand that motor power factor is never 100%.

As to how to get a motor power factor out of the information provided, no clue.

Cheers, Wayne
 
You need the voltage, the current, and the power factor or power factor angle to answer the question.

1 horsepower is defined as 746W. That is your 'power out'.

Apparent power is simply voltage * current, which you've calculated as 208 * 8.8A. And it seems like 746 / (208 * 8.8) = 40.7% which is supposedly the correct answer...but that is not the correct answer because motors have a power factor.
 
teeg123 said:
What is the efficiency and power factor of a one horsepower, single phase, 208-volt motor?
Click to expand...

teeg123 said:
What is the efficiency and power factor of a one horsepower, single phase, 208-volt motor?
Click to expand...
Is the answer supposed to be simply the Eff and PF combined, or do you need each individual component.

I would say you needed to find Eff X PF as found by Wayne in post #6 paragraph 1.
Very straight forward, don't read more into questions than there is. Don't assume information not provided.
 
You must log in or register to reply here.
Top