**CALCULATING
THE RESISTANCE OF A CONDUCTOR = {K} **

[ APPROXIMATE K & EXACT K ]

** Approximate K** = 12.9 for copper.

** Approximate K** = 21.2 for aluminum.

** Exact
K** = Resistance multiplied by the Circular Mill and then divided
by one thousand. You will find resistance of a wire and the circular mill
in NEC Chapter 9 Table 8.

**Special
Notes: **In
short for calculations during testing always use exact K instead of approximate
K to be safe. It does not take that long to use exact K and this may save
you from losing some score points due to exact K being required without
your knowledge.

** Example**:

[Written Form]

“Exact K” of a # 8, uncoated, stranded, aluminum conductor, is found in the NEC chapter 9, table 8. A # 8 stranded uncoated aluminum conductor is 1.28 ohms X 16,510 circular mills. Now, divide that by 1,000 = 21.1328 ohm. This is your “exact K” of the above mentioned # 8, uncoated, stranded, aluminum conductor.

Using the NEC chapter 9 table 8 to find the exact K of a conductor, look for the size column, then look down that column to the line stating the size for Awg. # 8. You will find two lines with Awg. # 8. Now look for the column for the stranding quantity. Then look down that column to # 8 again. You will find a line for 1 strand, which would be for solid, and a line for 7 strands, which would be for stranded. You want stranded {7strands} in this example. Now, go to the column for aluminum, and then look down that column for a sub-column like the one under copper, coated or uncoated. You will find none. Therefore, you want the only aluminum column present. Now, look down that aluminum column to Awg. # 8 line, on the same line as the Quantity of 7 strands, and then look back over to the aluminum column, and you will find 1.28 ohm resistance, in the aluminum column across the same line in the chart as the quantity of 7 strands. Now, look in the column for the area in circular. mills, and look down that column to the Awg. # 8, with the quantity of 7 strands, and you will find 16,510 mills. Now, multiply the 1.28 ohms by the 16,510 circular. mills, the product of that calculation equals 21,132.8 ohms. Now, divide 21,132.8 ohms by 1,000 to get the value of exact K which equals 21.1328 K. The results of that calculation is your exact K, on this Occasion.

**Special
Notes: ** The
column for coated refers to a coating found over the conductor that you
probably noticed in shop in junior high school when you built a motor by
wrapping wires around an iron core. This wire had a lacquer style coating “coated”

**Same Example**;

[Numeric Form]

The “Approximate K” of a # 8 uncoated aluminum stranded conductor = **21.2 “Approximate
K”**

The “Exact K” of a # 8 uncoated aluminum stranded conductor =** **

NEC Chapter 9 Table 8 =

1.28 X 16,510
divided by 1,000 = **21.1328 “Exact K”**

** Example Results; **

Therefore, “approximate K” is different from “exact K”. You will not be sure when the authors of a test will want you to use “exact K”. Most of the time, you will find both answers for you to mark. Mark the wrong one, and you will lose points of your test score. If the properties of the conductor {cu. or al.} and the conductor size is known, “use exact K”.

** Don’t
take a chance. Use only “exact K” during testing !**

CALCULATIONS FOR VOLTAGE DROP OF A FEEDER, OR A BRANCH CIRCUIT

**Special
Notes:** The FPN
Notes in the NEC are
considered to be advisory, only.

If you adhere to the NEC requirement considering voltage drop.

The NEC requires the conductor to be able to carry the load, as per Article 220 PARTS B & C & D for feeders, and as per Article 210-19 for branch circuit conductors. Article 220 parts B, C, & D, calculates the load on a conductor at 100% for a non- continuous load, and at 125% for continuous load

** PERIOD**.

The NEC speaks nothing about giving a break for consideration of a loss of power, due to a voltage drop, that decreases the current carrying capacity of the conductor used. Therefore the NEC expects a full amount of power, [voltage], at “end of line”.

Therefore the NEC requires that there will be no voltage drop allowance at all. You will find in ARTICLE 90-4 in the NEC that “judgment calls” are up to the Authority Having Jurisdiction. Therefore, the Authority Having Jurisdiction has the authority to allow the use of the FPN note speaking of 3% on a branch, or feeder, and with a total voltage drop of 5% on the feeder, and branch combined. This NEC FPN Note can be used as an allowance for you to use that is within the authority of his judgment. Otherwise the NEC flat says that the conductor must be able to carry the load as computed in Article 220.

**Special
Note:** In your voltage drop calculations you will find
the number 2 substituted by 1.732. When changing from a single phase to
a three phase calculation. The 2 [single phase] represents the wire going
to the load plus the wire coming back from the load to the grounded source.
[Not grounding] The same principle is used in the 1.732 [three phase] calculation.
The 1.732 figure representing the three wires used to run a three phase
motor is the square root of the 3 conductors.

** Power
Loss = ** Voltage drop x load in amps**.**

**Example**;

[Written Form]

120 volts with a feeder voltage drop of 3 % as per the NEC allowance in the FPN note NEC 215-2-b FPN note 2 =116.4 volts

**Same Example**;

[Numeric Form]

**120
volts x 3% VD allowed=3.6 volts of power loss; 120 volts - 3.6 volts=116.4
volts **

120 volts at source - 3.6 volts at end of line due to the

power loss = 116.4 volts applied at end of line

**Example Results; **

Due to resistance of the conductor we threw away 3.6 volts of power in this occasion, yet we have to pay for that voltage we did not get due to the voltage loss.

If we had a 1/2 horsepower motor designed to run on 120 volts, nominal, with a F.L.C. of 9.8 amp as per NEC Table 430-148, and we lost the 3.6 volts due to a long distance run causing the above calculated voltage drop this motor would now be pulling at the full load amps as follows;

**Special
Notes: ** You must change the Amps into Volt-Amps, in order
to accomplish the conversion, in the change of voltage, due to the voltage
drop calculated above.

9.8 AMPS x 120 VOLTS = 1,176 VOLT AMPS

1,176 VA DIVIDED BY 116.4 VOLTS AT END OF LINE = 10.103 AMPS

Formula to change amps into approximate volt - amps = amps x volts = volt amps

The results of the increase in motor load Amps and the loss of horse power due to the loss of voltage that is required to do the same work as the motor is designed to do without the voltage loss would cause an increase in cost, heat build up of the motor, loss of horse power, loss of life expectancy of the motor, etc.

As you can see voltage drop plays a big part in the

“ Art of Electricity ”

** Calculating
Conductor Properties as Relating to Voltage Drop **

** In
order to find the VOLTAGE DROP **

** Use
the following; **

**Voltage Drop [ VD ]
{single phase} = 2 [**representing
single phase] {which is the wire going out to the load <hot wire>,
and the wire going back to the source <grounded wire> 120 volt, or
two hot wires going to the load 240 volt, either style 120/240 volt making
up the reference “2”}. That 2 is multiplied by the resistance {K}
[using exact {K} for copper, or for aluminum calculated, by
you, using the NEC chapter 9 table 8 {normally uncoated if copper}].That
is multiplied by the length {L} [The total distance of the circuit
from the source to the load]. That is multiplied by the load
measured in amps {I}.

Then, divide the total of all of the above answer, by the Circular Mill {wire size }. This {C M } using (1 for solid or 7 for stranded) is found in the NEC Chapter 9

Table 8 which is wire size of the feeder, or branch circuit being calculated.

**FORMULA TO FIND VOLTAGE DROP {V D} ;**

** {exact}
2x K x L x I
CM **

**Voltage Drop [ VD ]
{three phase} =
1.732 [**representing three phase] {which is the square
root of the three wires going out to the load <hot wires>, making up
the 1.732}, That 1.732 is multiplied by the resistance {K}
[using exact {K} for copper or for aluminum calculated, by you,
using the NEC chapter 9 table 8 {normally uncoated if copper}].
That is multiplied by the length {L} [The total distance of
the circuit from the source to the load]. That is multiplied
by the load measured in amps {I}.

Then, divide the total answer of all of the above, by the Circular Mill {wire size }. This {C M } using (1 for solid or 7 for stranded) is found in the NEC Chapter 9

Table 8 which is the wire size of the feeder, or branch circuit being calculated.

**FORMULA TO FIND VOLTAGE DROP {V D} ;**

{exact}

1.732 x K x L x I

CM

** In
order to find the WIRE SIZE required considering
voltage drop **

** Use
the following; **

**Voltage Drop [wire
size] {single phase} {Circular
Mill / CM} = 2 [**representing
single phase] {which is the wire going out to the load <hot
wire>, and the wire going back to the source <grounded wire>120
volt, or two hot wires going to the load 240 volt, either style 120/240
volt making up the reference “2”}. That 2 is multiplied by the resistance
{K} [using approximate {K} of 12.9 for copper and 21.2 for
aluminum] (“Special
Note” in this case you do not know the Circular Mill in order to calculate
exact {K}). That is multiplied by the length {L} [The
total distance of the circuit from the source to the load]. That
is multiplied by the load measured in amps {I}.

Then, divide the total all of the above answer, by the voltage drop permitted. This {VD Permitted} is found in the NEC 215-2-B FPN Note 2 which is 3% allowed on a feeder circuit only or 3% allowed on a branch circuit only, or 5% total for the feeder, and branch circuits combined.

**FORMULA TO FIND CIRCULAR MILL {wire size} ;
**

{approx.}

**2x {K} x L x I**

** Voltage Drop Permitted**

**Voltage Drop [wire
size] {three phase} {Circular
Mill / CM} = ** Multiply **1.732
[**representing three phase] {which is the square root
of the three wires going out to the load <hot wires>, making up the
1.732},That 1.732 is multiplied by the resistance {K} [using
approximate {K} of 12.9 for copper and 21.2 for aluminum] (“Special
Note” in this case you do not know the Circular Mill in order to calculate
exact {K}). That is multiplied by the length {L} [The
total distance of the circuit from the source to the load]. That
is multiplied by the load measured in amps {I}.

Then, divide the total answer of all of the above, by the voltage drop permitted. This {VD Permitted} is found in the NEC 215-2-B FPN Note 2 which is 3 % allowed on a feeder circuit only, or 3 % allowed on a branch circuit only, or 5% total for the feeder, and branch circuits combined.

**FORMULA TO FIND Circular MILL {wire size} ;**

{approx.}

** 1.732x {K} x L x I
Voltage
Drop Permitted**

** In
order to find the maximum load allowed considering
voltage drop **

**Use
the following; **

** Voltage Drop [load]
{single phase} {load
/ I }** = [The Circular mill found in NEC chapter
9 table 8 , using {1 for solid or 7 for stranded}, for the wire size you
are using] multiplied by the voltage drop permitted This {VD Permitted}
is found in the NEC 215-2-B FPN Note 2 which
is 3% allowed on a feeder circuit only, or 3 % allowed on a branch circuit
only, or 5% total for the feeder, and the branch circuits combined.

Then, divide the total answer of all of the above by the total answer of the following;

Multiply **2 [**representing single phase] {which
is the wire going out to the load <hot wire>, and the wire going back
to the source <grounded wire>120 volt, or two hot wires going to the
load 240 volt, either style 120/240v making up the referance“2”}, That
2 is multiplied by the resistance {K} [using exact {K} for copper,
or for aluminum calculated, by you, using the NEC chapter
9 table 8 {normally uncoated if copper}]. That is then, multiplied by
the length {L} [The total distance of the circuit from the source
to the load].

** FORMULA TO FIND LOAD {LOAD} {I} ; **

** CM x Voltage Drop Permitted
2 x K x L
**{exact}

** Voltage
Drop [load] {three
phase} {load / I } = **CM
[The Circular mill found in NEC chapter 9 table 8, using {1
for solid or 7 for stranded}, for the wire size you are using] multiplied
by the voltage drop permitted. This {VD Permitted} is found in the NEC
215-2-B FPN Note 2 which is 3% allowed on a feeder circuit only, or 3 % allowed
on a branch circuit only, or 5% total for the feeder, and the branch circuits
combined.

Then, divide the total answer of all of the above by the total answer of the following;

Multiply **1.732 [**representing three phase] {which
is the square root of the three wires going out to the load <hot wires>,
making up the 1.732}, multiplied by the resistance {EXACT}{K}
[calculated, by you, using the NEC chapter 9 table 8 {normally
uncoated}]. That is then, multiplied by the length {L} [The
total distance of the circuit from the source to the load].

** FORMULA TO FIND LOAD {LOAD} {I} ;**

** CM x Voltage Drop Permitted
1.732 x K x L
{exact} **

** In
order to find the maximum distance allowed considering **

** voltage
drop Use the following; **

** Voltage Drop [distance]
{single phase} {L}
= **CM [The Circular mill found in NEC chapter 9 table
8 using {1 for solid or 7 for stranded}, for the wire size you are using]
multiplied by the voltage drop permitted This {VD Permitted} is
found in the NEC 215-2-B FPN Note 2 which is 3% allowed on a feeder circuit,
or 3 % allowed on a branch circuit only, or 5% total for the feeder circuit,
and the branch circuit combined.

Then, divide the total answer of all of the above by the total answer of the following;

Multiply 2 [representing single phase] {which is the wire going out to the load <hot wire>, and the wire going back to the source <grounded wire> 120 volt, or two hot wires going to the load 240 volt, either style 120/240v, making up the reference “2”}, multiplied by the resistance {EXACT}{K} [using exact {K} for copper, or for aluminum calculated, by you, using the NEC chapter 9 table 8 {normally uncoated if copper}]. That is then, multiplied by the load {I } [The total load on the circuit in amps].

**FORMULA TO FIND ; [distance]
{single phase} {L} **

** CM x Voltage Drop Permitted
2 x K x I**

** Voltage Drop [distance]
{three phase} {I } = ** CM
[The Circular mill found in NEC chapter 9 table 8 using {1
for solid or 7 for stranded}, for the wire size you are using] multiplied
by the voltage drop permitted This {VD Permitted} is found in the
NEC 215-2-B FPN Note 2 which is 3% allowed on a feeder circuit, or 3 % allowed
on a branch circuit only, or 5% total for the feeder circuit, and the branch
circuit combined.

Then, divide the total answer of all of the above by the total answer of the following;

Multiply **1.732 [**representing three phase] {which
is the square root of the three wires going out to the load <hot wires>,
making up the 1.732}, multiplied by the resistance {K} [using
exact {K} for copper, or for aluminum calculated, by you, using
the NEC chapter 9 table 8 {normally uncoated if copper}].
That is then, multiplied by the load {I } [The total load on
the circuit in amps].

** FORMULA TO FIND [distance] {single
phase} {L} ; **

** CM x Voltage Drop Permitted
1.732 x K x I **

This document is based on the 1999 national electrical code and is designed to give you an option, as a self-help, that should pass minimum code requirements. While extreme care has been implemented in the preparation of this self-help document, the author and/or providers of this document assumes no responsibility for errors or omissions, nor is any liability assumed from the use of the information, contained in this document, by the author and / or provider.

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