8. The unit of electrical resistance, now universally adopted, is called the international ohm. One international ohm is the resistance offered by a column of pure mercury 106.3 centimeters in length and 1 square millimeter in sectional area at 32° F., or the temperature of melting ice. The dimensions of the column expressed in inches are as follows: length 41.85 inches, sectional area .00155 square inch. Hereafter, the word "international" will be omitted, and simply the word "ohm" used; the international ohm, however, as defined above, will always be implied unless otherwise stated.

9. In Table 1 are given various data respecting the copper wire used in electrical installations. In the first column is the gauge number by American Wire Gauge; in the second column is the diameter as measured in mils (one mil = one one-thousandth of an inch); the third column shows the area of cross-section in circular mils. It is usual to adopt this method for a round wire, instead of the old way of expressing the area in fractions of a square inch, in which case the diameter is squared and the product multiplied by .7854, as explained in Geometry and Mensuration. If the second operation be omitted, and the diameter, as measured in thousandths of an inch, be only squared (or multiplied by itself), the result is expressed in circular thousandths, or circular mils.

Example

What is the area in circular mils of a wire 2 1/2 inches in diameter ?

Solution

2 1/2 in. = 2,500 mils. 2,5002 = 2,500x2,500 = 6,250,000 circular mils. Ans.

The resistance of copper wire being low, a unit length of 1,000 feet is usually taken in tables of resistance, and this unit is considered in the eighth column.

10. The resistance of a given conductor increases as the length of the conductor increases; that is, the resistance is directly proportional to the length of the conductor. For example, if the length of a conductor be doubled, its resistance will be doubled.

The resistance of any length of conductor may be found by the following formula:

R = LR1

1,000'

(3.) where R = required resistance; L = length of conductor; R1 = resistance per 1,000 feet of conductor.

Table 1. American, Or B. & S., Gauge

Gauge No.

Diameter

Mils (d).

1 Mil = .001 In.

Area.

Weight and Length.

Resistance. Ohms per 1,000 Feet.

Current Allowed. Amperes

Gauge No.

Circular Mils

Square

Inches

(d2X.7854).

Pounds per 1,000

Feet.

Pounds per

Mile.

Feet per

Pound.

0000

460.000

211,600.00

.1661900

639.33

3,375.700

1.56

.051

175

0000

000

409.640

167,805.00

.1317900

507.01

2,677.000

1.97

.064

145

000

00

364.800

133,079.00

.1045200

402.09

2,123.000

2.49

.081

120

00

0

324.950

105,592.00

.0829320

319.04

1,684.500

3.13

.102

100

0

1

289.300

83,694.00

.0657330

252.88

1,335.200

3.95

.129

95

1

2

257.630

66,373.00

.0521300

200.54

1,058.800

4.99

.163

70

2

3

229.420

52,634.00

.0413390

159.03

839.680

6.29

.205

60

3

4

204.310

41,742.00

.0327840

126.12

665.910

7.93

.259

50

4

5

181.940

33,102.00

.0259980

100.01

528.050

10.00

.326

45

5

6

162.020

26,250.00

.0206170

79.32

418.810

12.61

.411

35

6

7

144.280

20,817.00

.0163490

62.90

332,110

15.90

.519

30

7

8

128.490

16.509.00

.0129660

49.88

263.370

20.05

.652

25

8

9

114.430

13,094.00

.0102840

39.56

208.880

25.28

.824

9

10

101.890

10,381.00

.0081532

31.37

165.630

31.88

1.040

20

10

11

90.742

8,234.10

.0064670

24.88

137.370

40.20

1.311

11

12

80.808

6,529.90

.0051286

19.73

104.180

50.69

1.653

15

12

13

71.961

5,178.40

.0040671

15.65

82.632

63.91

2,084

13

14

64.084

4,106.80

.0032254

12.41

65.525

80.59

2.628

10

14