A nematic liquid-crystal cell subject to an electric field created by electrodes held at constant potential is modeled as a variable capacitor in an RC circuit. The state of the system is characterized in terms of the director field in the cell and the charge on the electrodes. A dynamical system is developed that couples director dynamics in the cell (with no fluid flow) and charge dynamics in the circuit. The dynamical equations are derived from expressions for the total potential energy of the system and a dissipation involving a single rotational viscosity for the director plus Joule heating associated with current in the circuit. An effort is made to quantify effects, in particular the widely differing time scales for the processes involved, and numerical illustrations are given. The exercise illuminates aspects of the modeling of equilibrium states of such a system.

受到由保持在恒定电位的电极产生的电场作用的向列液晶单元被建模为 RC 电路中的可变电容器。系统状态的特征在于电池中的指向矢场和电极上的电荷。开发了一个动力系统，它将电池中的导向器动力学（没有流体流动）与电路中的电荷动力学耦合。动力学方程源自系统总势能的表达式，以及涉及指向矢的单一旋转粘度加上与电路中的电流相关的焦耳热的耗散。努力量化影响，特别是所涉及过程的广泛不同的时间尺度，并给出了数值说明。