Resistor-Capacitor Circuit as a Dynamic System  

作　　者：Slavko Đurić Slavko Đurić(Faculty of Transport and Traffic Engineering Doboj, University of East Sarajevo, Doboj, Bosnia and Herzegovina)

机构地区：[1]Faculty of Transport and Traffic Engineering Doboj, University of East Sarajevo, Doboj, Bosnia and Herzegovina

出　　处：《Journal of Applied Mathematics and Physics》2024年第10期3307-3314,共8页应用数学与应用物理（英文）

摘　　要：The paper considers the response to the accumulated energy in the resistor (R)-capacitor (C) circuit. In the (RC) circuit, the capacitor C is initially charged with the “capacitive” voltage U0. At that moment t=0, the P circuit switch turns on. By using Kirchhoff’s laws on the elements, a homogeneous differential equation of the first order with constant coefficients is obtained with the initial condition UC(0)=U0. The solution of the differential equation is presented in exponential form UC(t)=U0⋅e−t/τ. Qualitative analysis RC of the circuit gives a phase portrait on the line. From the phase portrait on the line, it can be seen that the charge UC(t)→UC∗=0when t→∞stabilizes, regardless of the initial conditions. It is shown that from UC(t)=U0⋅e−t/τa dynamic system defined by the function φ(t,UC)=UC⋅e−t/τcan be formed from. It has also been shown that, from the formed dynamic system, an autonomous system (circuit equation RC) can be found whose solution describes the formed dynamic system. It is also shown that the dynamic system φ(t,UC)=UC⋅e−t/τhas one attractive fixed point UC=0.The paper considers the response to the accumulated energy in the resistor (R)-capacitor (C) circuit. In the (RC) circuit, the capacitor C is initially charged with the “capacitive” voltage U0. At that moment t=0, the P circuit switch turns on. By using Kirchhoff’s laws on the elements, a homogeneous differential equation of the first order with constant coefficients is obtained with the initial condition UC(0)=U0. The solution of the differential equation is presented in exponential form UC(t)=U0⋅e−t/τ. Qualitative analysis RC of the circuit gives a phase portrait on the line. From the phase portrait on the line, it can be seen that the charge UC(t)→UC∗=0when t→∞stabilizes, regardless of the initial conditions. It is shown that from UC(t)=U0⋅e−t/τa dynamic system defined by the function φ(t,UC)=UC⋅e−t/τcan be formed from. It has also been shown that, from the formed dynamic system, an autonomous system (circuit equation RC) can be found whose solution describes the formed dynamic system. It is also shown that the dynamic system φ(t,UC)=UC⋅e−t/τhas one attractive fixed point UC=0.

关 键 词：RC Circuit VOLTAGE Dynamic System 

分 类 号：O17[理学—数学]