# 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

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.

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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