Voltage drop

[Brafs4411]

A question from my Mike holt book,
A 240v,24A,single phase load is located 100 ft from the panel board and is wired with 10AWG. What is the voltage drop of the circuit conductors?

Answer in book is 5.76V
1.20 ohms per 1000 foot the calculation result says.
10awg 1.240 ohms per 1000 ft

1.240÷1000=.00124
.00124×200ft=.248
.248 ×24A=5.952.

Why does the book round the numbers.

 

[gar]

180718-2034 EDT

Why not? Do you really expect to know what the resistance is to 1 part in 1000. Diameter variation, alloy, and temperature are somewhat unknown variable factors. One internet table shows 1.215 at 75 deg C, and 1.000 at 20 deg C.

Note: every change of three wire sizes produces a resistance change by a factor of 2.

#10 --- 1 ohm
#13 --- 2 ohms
#16 --- 4 ohms

#11 --- 1.25 ohms rounded down
#12 --- 1.6 ohms rounded up

1.25*1.6 = 2.000 so this comes out nice


.

 

[gar]

180719-2513 EDT

The accurate resistance ratio from one wire number to the next is the cube root of 2. This is approximately 1.2599 .

.

 

[winnie]

If we are going to be pedantic, the accurate resistance ratio from on wire size to the next is the 2/39th root of 92. *grin*

Seriously gar's main point is key: you don't exactly know the resistance of the wire for any number of reasons, and expressing the voltage drop answer with too many 'significant digits' implies that you know more than you really do.

If I say something is 1 foot long, that means something different than saying it is 12.000 inches long. The 'nominal' values are exactly the same, but the second expression (12.000 inches) implies a much more accurate measurement.

-Jon

 

[ggunn]

If we are going to be pedantic, the accurate resistance ratio from on wire size to the next is the 2/39th root of 92. *grin*

Seriously gar's main point is key: you don't exactly know the resistance of the wire for any number of reasons, and expressing the voltage drop answer with too many 'significant digits' implies that you know more than you really do.

If I say something is 1 foot long, that means something different than saying it is 12.000 inches long. The 'nominal' values are exactly the same, but the second expression (12.000 inches) implies a much more accurate measurement.

-Jon

What he said. When you do a calculation using numbers of differing significant digit counts, the answer is only good to the quantity of digits as the entry with the least SDs.

 

[zbang]

Why does the book round the numbers.

I didn't write the book, but such precision doesn't matter for the work most of us do. We could say 120 volts, 119 volts, or 118.37 volts, but for the vast majority of application it doesn't matter at all. Is it a 9.6 amp load or a 10.2 amp load? Usually doesn't matter because you're not running both of them (continuously) on a 20 amp breaker anyway. That kind of thing.

Or, sometimes "close enough" really close enough .

 

[Ingenieur]

A question from my Mike holt book,
A 240v,24A,single phase load is located 100 ft from the panel board and is wired with 10AWG. What is the voltage drop of the circuit conductors?

Answer in book is 5.76V
1.20 ohms per 1000 foot the calculation result says.
10awg 1.240 ohms per 1000 ft

1.240÷1000=.00124
.00124×200ft=.248
.248 ×24A=5.952.

Why does the book round the numbers.

NEC
DC R 1.2
AC Z 1.1
if you use their R and X (steel) ~ 1.2017 or 1.2010 (pvc or alum)

where did the 1.24 come from?

 

[ggunn]

I didn't write the book, but such precision doesn't matter for the work most of us do.

It isn't precision to have a number with seven digits where only the first three are significant. The last four digits are random numbers.

We use PVWatts a lot to estimate the projected output of a PV system. It reports the yearly kWh production results down to the last kWh; for a large-ish system this could be a six or seven digit number, but then it says the error bars are +/- 10%. Most of the digits in the projected number are junk.

 

[sameguy]

We round them because if you square them that makes the new number really big!
Try it, take the number 4.25 and square it, see much bigger than rounding.

 

[Murphy79]

A question from my Mike holt book,
A 240v,24A,single phase load is located 100 ft from the panel board and is wired with 10AWG. What is the voltage drop of the circuit conductors?

Answer in book is 5.76V
1.20 ohms per 1000 foot the calculation result says.
10awg 1.240 ohms per 1000 ft

1.240÷1000=.00124
.00124×200ft=.248
.248 ×24A=5.952.

Why does the book round the numbers.

I the formula is 2*L*R*I/1000 =VD
or

2*100*1.21( chapter9 table8 for conductor properties of #10 copper....uncoated ohm/ft)*24= 5808/1000= 5.8 Volts

Next, 5.808v/240v= .0242*100( so we can make this a percentage)= 2.42%

which is less than 3%


You could have also excluded the previous step and saw that 5.808 would have gave you the answer.....because 3% of 240V is 7.2V....I don't know why the short explanation was given...In my opinion,It is important to fully understand the equations before taking short cuts

 

[Murphy79]

NEC
DC R 1.2
AC Z 1.1
if you use their R and X (steel) ~ 1.2017 or 1.2010 (pvc or alum)

where did the 1.24 come from?

Also use quantity of #1 for Chapter 9 table 8...as it is for a single solid conductor....the 7 represents stranded conductors.

 

[broadgage]

Also remember that within living memory, that electricians had to calculate voltage drop BY HAND with pencil and paper, before the advent of cheap electronic calculators, or cell phones incorporating a calculator.
Such calculations had to be relatively simple and not involve needless significant digits.

In the UK and I presume elsewhere, many rules of thumb existed to eliminate calculations on small and simple installations.

"for lighting in a normal size house, no more than a dozen (15 if you are satisfied that some are very low use) lamps per 5 amp 240 volt circuit. 3/.029 cable is fine for any likely circuit in a normal size house"

"For ring circuits for general purpose power, use 7/.029 cable on a 30 amp fuse. No limit on number of outlets provided that the floor area does not exceed 100 square yards, AND that the total length of cable does not exceed 100 yards."

Millions of homes were wired thus, without any calculation whatsoever, and a lot still are.

 

[hbiss]

A question from my Mike holt book,
A 240v,24A,single phase load is located 100 ft from the panel board and is wired with 10AWG. What is the voltage drop of the circuit conductors?

Answer in book is 5.76V
1.20 ohms per 1000 foot the calculation result says.
10awg 1.240 ohms per 1000 ft

1.240÷1000=.00124
.00124×200ft=.248
.248 ×24A=5.952.

Why does the book round the numbers.

Where do you see rounding? Because 1.20/1000 is given and you found 1.24 someplace? If you want the correct answer and pass the test you have to use whatever information is given.

Check your work-

1.20÷1000=.00120
.00120×200ft=.240
.240 ×24A=5.76.

-Hal