Fuse Equations

Fuse Equations (Preece’s Law)

Preece’s Law can be used to generate an estimate for the approximate dc fusing current for a given wire size and material. The actual fusing current can unfortunately depend on the detailed heat transfer from the wire which can be influenced by the enclosure, conduction of heat through the wire to the terminals on both ends, and other physical conditions. A one-dimensional heat equation or more complicated thermal analysis can therefore be used to better determine the exact fusing current. However, as a quickly determined estimate, Preece’s Law can be valuable.

Preece’s Law states that the dc fusing current for a straight wire element generally depends upon it’s diameter as given by:

 

Preeces Law equation to determine fusing current for a given wire diameter and Preece's coefficient, dependent upon fuse element metal

Preeces Law

Or, one can determine the wire diameter for a given material and fusing current so that a larger size wire can be selected to avoid fusing.

Preeces Law equation to determine required fuse element diameter based on desired fusing current and Preece's coefficient, dependent upon fuse element metal

where If is the fusing current in amps, C is Preece’s Coefficient for the particular metal in use, and d is the fuse element diameter in inches. William Henry Preece determined this relationship in 1884 by comparing the balance between the heat generated within wire (I²R) to the heat loss from the wire  (πhdl) where h is the heat loss per unit area from radiation or convection, d is the wire diameter, and l is the wire length (6″ long in the case of the test samples that Preece used to empirically determine this). Near the fusing threshold, the heat loss and heat generated are approximately equal. So we can set the heat generated equal to the heat dissipation as follows:

Solving for I², we determine:

We can then take the square root to solve for the fusing current as a function of the wire diameter (as above):

Where C is Preece’s coefficient depending upon the specific wire material/alloy:


The following table shows Preece’s Coefficients for common fuse element materials/alloys as well as the diameter of wires of these materials which will be fused by the given current in the table.

 


Diameters (Inches)

Current (A)

Copper

C=10,244


Aluminum

C=7,585


Platinum

C=5,172


German Silver

C=5,230


Platinoid

C=4,750

1

0.0021


0.0026


0.0033


0.0033


0.0035

2

0.0034


0.0041


0.0053


0.0053


0.0056

3

0.0044


0.0054


0.007


0.0069


0.0074

4

0.0053


0.0065


0.0084


0.0084


0.0089

5

0.0062


0.0076


0.0098


0.0097


0.0104

10

0.0098


0.012


0.0155


0.0154


0.0164

15

0.0129


0.0158


0.0203


0.0202


0.0215

20

0.0156


0.0191


0.0246


0.0245


0.0261

25

0.0181


0.0222


0.0286


0.0284


0.0303

30

0.0205


0.025


0.0323


0.032


0.0342

35

0.0227


0.0277


0.0358


0.0356


0.0379

40

0.0248


0.0303


0.0391


0.0388


0.0414

45

0.0268


0.0328


0.0423


0.042


0.0448

50

0.0288


0.0352


0.0454


0.045


0.048

60

0.0325


0.0397


0.0513


0.0509


0.0542

70

0.036


0.044


0.0568


0.0564


0.0601

80

0.0394


0.0481


0.0621


0.0616


0.0657

90

0.0426


0.052


0.0672


0.0667


0.0711

100

0.0457


0.0558


0.072


0.0715


0.0762

120

0.0516


0.063


0.0814


0.0808


0.0861

140

0.0572


0.0698


0.0902


0.0895


0.0954

160

0.0625


0.0763


0.0986


0.0978


0.1043

180

0.0676


0.0826


0.1066


0.1058


0.1128

200

0.0725


0.0886


0.1144


0.1135


0.121

225

0.0784


0.0958


0.1237


0.1228


0.1309

250

0.0841


0.1208


0.1327


0.1317


0.1404

275

0.0897


0.1095


0.1414


0.1404


0.1497

300

0.095


0.1161


0.1498


0.1487


0.1586

 


Diameters (Inches)

Current (A)

Iron

C=3,148


Tin

C=1,642


Tin-Lead

C=1,318


Lead

C=1,379

1

0.0047


0.0072


0.0083


0.0081

2

0.0074


0.0113


0.0132


0.0128

3

0.0097


0.0149


0.0173


0.0168

4

0.0117


0.0181


0.021


0.0203

5

0.0136


0.021


0.0243


0.0236

10

0.0216


0.0334


0.0386


0.0375

15

0.0283


0.0437


0.0506


0.0491

20

0.0343


0.0529


0.0613


0.0595

25

0.0398


0.0614


0.0711


0.069

30

0.045


0.0694


0.0803


0.0779

35

0.0498


0.0769


0.089


0.0864

40

0.0545


0.084


0.0973


0.0944

45

0.0589


0.0909


0.1052


0.1021

50

0.0632


0.0975


0.1129


0.1095

60

0.0714


0.1101


0.1275


0.1237

70

0.0791


0.122


0.1413


0.1371

80

0.0864


0.1334


0.1544


0.1499

90

0.0935


0.1443


0.1671


0.1621

100

0.1003


0.1548


0.1792


0.1739

120

0.1133


0.1748


0.2024


0.1964

140

0.1255


0.1937


0.2243


0.2176

160

0.1372


0.2118


0.2452


0.2379

180

0.1484


0.2291


0.2652


0.2573

200

0.1592


0.2457


0.2845


0.276

225

0.1722


0.2658


0.3077


0.2986

250

0.1848


0.2851


0.3301


0.3203

275

0.1969


0.3038


0.3518


0.3417

300

0.2086


0.322


0.3728


0.3617


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