Effects of temperature, AC fields and nonlinearity

In a first approach, we take again the picture of the infinite cluster as a super-lattice. If zl is the current in a link, the change AT in the temperature of the bonds in the link will be proportinal to i Rh, where Ri, is the link resistance. In c = 2, we have zl = i/L)I and R Ri, where I is the total current through the sample. One thus gets 

In a second approach, the picture of a link between two nodes of an infinite cluster will be made more precise by introducing the blobs. In a link, the bonds with the largest current (in fact the total current flowing through the link) are the singly connected (sc) bonds. The new melting criterion is applied only to these bonds, by writing 

In conclusion, the two criteria, namely that the current in a link or that the temperature of a singly-connected bond reaches a specific value at the failure, give the same results. It was in fact expected, since the two quantities ATgc and ii, are related by the relation (2.43). We shall see below the experimental results giving support for the second approach and making the fuse model a realistic one. 

Suppose a current I flows through a sample of resistance Rq. Rq is defined as the resistance of the sample at zero current. Because of the Joule effect, the resistance will increase by AR = Rof3AT, where (3 is the temperature coefficient of the resistance. As above, one can write AT rsj RqP, and this approximation therefore gives AR Rol) , The voltage V across the sample is therefore given by 

The voltage is thus a sum of two parts one with the same frequency as that of the applied current and the other with a frequency three times the original frequency - the so called third harmonic. The third harmonic coefficient B is defined as B = Vs//(7o).  

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