论文标题
通用电容器的电荷电压关系
Charge-voltage relation for a universal capacitor
论文作者
论文摘要
大多数电容器不满足常规的恒定电容假设。它们表现出记忆，通常通过随时间变化的电容来描述。结果表明，经典关系，$ q \ left（t \右）= cv \ left（t \右）$，将费用，$ q $与电容，$ c $，$ c $，$ c $，$ v $相关联，不适用于与时间变化的电容器。当前的$ dq/dt $的表达式随后在经典关系中用$ c \ left（t \右）$替换为$ c $后获得的表达式对应于不一致的电路。为了解决不一致的情况，我提出了一种电荷 - 电压关系，该电容器上的电荷是通过其时间变化的电容与使用的一阶时间衍生的卷积表示，即应用电压的一阶时间衍生，即$ q \ q \ weft（t \ right）= c \ weft（t \ weft（t \ weft \ right）\ aST $ dv $ dv $ dv $ dv $ dv $ dv $ dv。这种关系对应于通用电容器，该电容器也称为分数演算社区中的分数电容器。由于分数电容器与世纪历史的Curie-von Schweidler法律表达的通用介电响应具有固有的联系，因此该发现也扩展到了介电的研究。
Most capacitors do not satisfy the conventional assumption of a constant capacitance. They exhibit memory which is often described by a time-varying capacitance. It is shown that the classical relation, $Q\left(t\right)=CV\left(t\right)$, that relates the charge, $Q$, with the capacitance, $C$, and the voltage, $V$, is not applicable for capacitors with a time-varying capacitance. The expression for the current, $dQ/dt$, that is subsequently obtained following the substitution of $C$ by $C\left(t\right)$ in the classical relation corresponds to an inconsistent circuit. In order to address the inconsistency, I propose a charge-voltage relation according to which the charge on a capacitor is expressed by the convolution of its time-varying capacitance with the first-order time-derivative of the applied voltage, i.e., $Q\left(t\right)=C\left(t\right)\ast dV/dt$. This relation corresponds to the universal capacitor which is also known as the fractional capacitor among the fractional calculus community. Since the fractional capacitor has an inherent connection with the universal dielectric response that is expressed by the century old Curie-von Schweidler law, the finding extends to the study of dielectrics as well.
