Aplicação da função de Lambert-Tsallis na solução de um circuito resistor-capacitor com decaimento não exponencial

Abstract

The present dissertation uses the Lambert-Tsallis Wq function in order to get the analytical solution for the non-exponential decay of the total electric current in an electric circuit, fed with a DC power supply, composed by two parallel branches of resistor-capacitor series circuits. The result obtained permits the analytical calculation of the half-life time of the total electrical current, that is, the time required for the total current to decay to half of its initial value. Following, it was shown that the solution for the half-life time of the total electrical current obeys a Fermat-type equation therefore, depending on the values chosen for the resistors and capacitors be algebraic or transcendental numbers, integers value larger than two for the half-life time can be forbidden or not. This is a physical example of the famous Fermat last theorem from number theory, as well it demonstrates a physical implication of the usage of algebraic and transcendental numbers. At last, it was presented the electronic circuit of an oscillator, named Fermat’s oscillator, whose oscillation period depends on the solution of the Fermat equation.