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**
**
Applying of differential equations with variable coefficients of Dirac
δ-functions to study of series RLC-circuits with discrete-continuum
characteristics**

**
A. B. Putilin, R. E. Liberzon, V. K. Kurbanaliev**

**
Moscow State University of Mechanical Engineering (MAMI)**

**
FSUE "Academician A.I. Berg **
**
CNIRTI****"**

The paper is received on December 15, 2014

**Abstract.
**The paper
explores the effects of pulsed changes in temperature on a
thermistor within a RLC circuit. The effects of
temperature were represented in Dirac δ-functions. The study establishes that the solution
lies in a differential equation with variable
coefficients of Dirac δ-functions. An accurate dimensionless criteria solution has been
obtained. An asymptotic representation of the
current function in the resonance circuit at low time values has been
constructed using the limit theorem. It has been proved that at certain time
values the current can exceed a well-defined expected value, which may
trigger the radio electronic system failure.

**Key words:** RLC circuit, thermistor, Dirac delta function, asymptotic
representation, system failure, radio electronic
system.** **