Complex Number Division Question

[jakesaround]

Hey all, its me again.

Here is probably an really easy question but I don't recall how to solve can you help?

This is taken from the 2009 NCEES Electrical Power Sample Questions #512

This is an NEC question but looking up the information in the code book I understand.

The question is basically asking what is the phase to neutral impedance for a given length of cable.

I was able to locate the R and X values from Chapter 9 table 9 in the NEC. Which gave me a complex number of;

0.035 + j0.049 ohms per 1000ft

Now the part that I am hung up on is the question asks for the impedance for just 500ft of conductor.

So my question is how do you divide the impedance 0.035 + j0.049 per 1000ft to get the impedance for this conductor at 500ft.

If anyone could give me a step by step process I would greatly appreciate it.

Thanks.

 

[Flyer_PE]

It's a number conversion.

1000ft of cable has an impedance of Z.

500 ft of cable has an impedance of Z/2.

Since, in this problem, you have two conductors in parallel, the impedance will be reduced by half again.

Final answer is that you have the impedance of 1000ft/(2x2) = Z/4.

In this example Z=0.035+j0.049

Z/4=0.035/4 + j0.049/4 = 0.0088 + j 0.0123

 

[jakesaround]

Thanks Flyer,

I think it was the parallel conductor that was throwing off my final answer.