how do i find Xl in the following question?
if i use the 10.9 answer as xl (thats given) then the total current wont equal 27.7 as stated in the question? where am i going wrong?

 

View attachment 328627
how do i find Xl in the following question?
if i use the 10.9 answer as xl (thats given) then the total current wont equal 27.7 as stated in the question? where am i going wrong?

 

and the value of the inductor is 0.03377586202 henry
Is it possible the given original answer to this question is not correct

 

and the value of the inductor is 0.03377586202 henry
Is it possible the given original answer to this question is not correct

The original looks correct to the three digits given anyway.

First, try converting the 10.9 Ohms into the inductor inductance value when f=50Hz.
Do you know how to do that?
Then calculate the line current. If you do that right, you get very close to the given value of 27.7 amps.
That would prove the answer given is correct. You can also use your "square root" formula to do this.
Then all you have to do is reverse your calculations to obtain that 10.9 Ohms, and it should come out close to that, within about 0.02 Ohms.

 

The original looks correct to the three digits given anyway.

First, try converting the 10.9 Ohms into the inductor inductance value when f=50Hz.
Do you know how to do that?
Then calculate the line current. If you do that right, you get very close to the given value of 27.7 amps.
That would prove the answer given is correct. You can also use your "square root" formula to do this.
Then all you have to do is reverse your calculations to obtain that 10.9 Ohms, and it should come out close to that, within about 0.02 Ohms.

You're Right the answer is correct. where i went wrong was i forgot to put a space in the calculator after square root 3 for Current Line.