7H0011X0 W&C Tech Handbook Sec 18

7/27/2019 7H0011X0 W&C Tech Handbook Sec 18

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18. FORMULAS

AND CONSTANTS18.1 Electrical Properties of Circuits 29

18.2 Resistance and Weight of Conductors 29

18.3 Resistance, Inductance and Capacitance in AC Circuits 29

18.4 Series and Parallel Connections 29

18.5 Engineering Notation 29

18.6 Diameter of Multiconductor Cables 29

18.7 Determination of Largest Possible Conductor in Cable Interstices 30

18.8 Conductor Diameter from Wire Diameter 30

18.9 Coaxial Capacitance 30

18.10 Inductive Reactance 30

18. Formulas and Constant

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18.1 ELECTRICAL PROPERTIES OF CIRCUITS

Table 18.1Electrical Properties of Circuits

cos Power factor of load (pf)V Volts between conductorsEff. Efficiency of motorI Current (amperes)

kw

KilowattskVA Kilovoltampereshp Horsepower

Alternating Current Direct Current

Desired Data Single Phase Three Phase

Kilowatts(kw)

I V cos 1,000

1.73 I V cos 1,000

I V1,000

Kilovolt-amperes(kVA)

I V1,000

1.73 I V1,000

I V1,000

Horsepoweroutput

I V cos Eff.746

1.73 I V cos Eff.746

I V Eff.746

Amperes (I) whenhorsepoweris known

hp 746V cos Eff.

hp 7461.73 V cos Eff.

hp 746

V Eff.

Amperes (I) whenkilowatts are

known

kw 1,000V cos

kw 1,0001.73 V cos

kw 1,000V

Amperes (I) whenkilovolt-amperesare known

kVA 1,000V

kVA 1,0001.73 V

kVA 1,000V

|18. Formulas and Constants

296 |


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18.2 RESISTANCE AND WEIGHT OF CONDUCTORS

The resistance and weight of any uncoated copper wire at 20C (68F) having a conductivity of 100 percent IACS may be calculated from the following formula

Ohms per 1,000 feet

Pounds per 1,000 feet Area in sq. in. 3,854.09 or area in cmils 0.0030269

18.3 RESISTANCE, INDUCTANCE AND CAPACITANCE IN AC CIRCUITS

Table 18.2Resistance, Inductance and Capacitance in AC Circuits

V Voltage in volts I Current in amperes L Inductance in henries f Frequency in cycles per secondR Resistance in ohms C Capacitance in farads 3.1416


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or

0.0081455

Cross-sectional area in sq. in.

10371.176

Cross-sectional area in cmils

If Circuit Contains Reactance Impedance V for Current I Power Factor

Resistance (R)Only

O R IR 1

Inductance (L)Only

2fL 2fL I2fL O

Capacitance (C)Only

12fC

12fC

I1 1

2fCO

Resistance andInductance inSeries (R and L)

2fL R2 (2fL)2 IR2 (2fL)2R

R2 (2fL)2

Resistance andCapacitance inSeries (R and C)

12fC

Resistance,Inductance andCapacitance inSeries (R, L and C)

2fL 1 1

2fC2fL

1 12fC( )

2

( )2

R2 + 2fL 1 1

2fC

( )2

12fC

( )2

R2 + 2fL 1

2fCR

R2 + ( )2

12fCR2 +I ( )

2

12fCR2 +

R


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298 |

R R1 R2 R3 +

1 1 1 1__ __ __ __R

R1

R2

R3

1 1 1 1__ __ __ __C

C1

C2

C3

1 1 1 1__ __ __ __L

L1

L2

L3

L L1 L2 L3 +

C C1 C2 C3 +

18.4 SERIES AND PARALLEL CONNECTIONS

Table 18.3Series and Parallel Connections

Resistance Inductance Capacitance(R) (L) (C)

Series

Parallel

18.5 ENGINEERING NOTATION

Table 18.4Engineering Notation

Multiplying Factor

Prefix Symbol Scientific Conventional

tera T 1012

1,000,000,000,000giga G 10

91,000,000,000

mega M 106

1,000,000

kilo k 103

1,000hecto h 10

2100

deca da 10

1

10deci d 10

-10.1

centi c 10-2

0.01milli m 10

-30.001

micro 10-6

0.000001nano n 10

-90.000000001

pico p 10-12

0.000000000001

femto f 10-15

0.000000000000001atto a 10

-180.000000000000000001


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Table 18.5Engineering Notation

e 2.7183

3.1416

2 1.4142

3 1.7321

/4 0.7854

1/C one conductor

3/C three conductor

greater than

less than or equal to

less than

greater than or equal to

18.6 DIAMETER OF MULTICONDUCTOR CABLES

To calculate the overall diameter of a group of round conductors of uniform diameters twisted together, multipy the diameter of an individual conductorby the applicable factor below.

Table 18.6Diameter of Multiconductor Cables

Number of Conductors Factor

1 1.0002 2.0003 2.155

4 2.4145 2.7006 3.000

7 3.0008 3.3109 3.610


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300 |

18.7 DETERMINATION OF LARGEST POSSIBLE CONDUCTOR IN CABLE INTERSTICES

The following factors permit the calculation of the maximum size conductor that will fit into the interstices (open spaces) of various conductorconfigurations, while keeping within a circumscribing circle. Multiply the diameter of one main conductor by the factor from the chart below to obtainthe largest diameter that will fit into the interstices.

Table 18.7Determination of Largest Possible Conductor in Cable Interstices

Number of Conductors Factor

2 0.6673 0.4834 0.4145 0.3776 0.354

18.8 CONDUCTOR DIAMETER FROM WIRE DIAMETER

To calculate the nominal diameter of any concentric-lay-stranded conductor made from round wires of uniform diameters, multiply the diameter of anindividual wire by the applicable factor below:

Table 18.8Concentric Stranded Conductor Diameter from Wire Diameter

Number of Wires Factor to Calculatein Conductor Conductor Diameter

3 2.1557 3.00012 4.155

19 5.00037 7.00061 9.000

91 11.00127 13.00169 15.00

217 17.00

271 19.00

For a greater number of wires use the formula: Conductor Diameter Wire Diameter 1.332 No. of Wires


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18.9 COAXIAL CAPACITANCE

C

Where:C is capacitance in picofarads per foote is the dielectric constant (also known as SIC)t is insulation thickness in milsd is diameter over the conductor (diameter under the insulation) in mils

Other forms of this equation include:

C1

or

C2

Where:C

1is capacitance in microfarads per 1,000 ft.

C2

is capacitance in microfarads per kilometere is the dielectric constantD is diameter over the insulationd is diameter under the insulation

18.10 INDUCTIVE REACTANCE

The inductive reactance of a shielded 3-conductor medium-voltage power cable at 60 Hz can be calculated with the following formulas:

XL 0.023 Ln ( ) ohms/1,000 ft.

or

XL 0.0754 Ln ( ) ohms/km

Where:GMD geometric mean distance (equivalent conductor spacing)GMR geometric mean radius of conductor

For conductors in a triplexed configuration, GMD is equal to the center-to-center spacing. For round, concentric stranded conductors, GMR rangesfrom 0.363d for a 7-wire strand up to 0.386d for a 61-wire strand where d is the diameter of the conductor.

GMDGMR

GMDGMR

Dd

0.0556e

Ln ( )

D

d

0.0169e

Ln

( )

7.354eLog

10(1 + 2t/d)


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7H0011X0 W&C Tech Handbook Sec 18