Fuse Equations
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:
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 |