Capacitor Charging Equation

电容器充电方程

The transient behavior of a circuit with a battery, a resistor and a capacitor is governed by Ohm's law, the voltage law and the definition of capacitance. Development of the capacitor charging relationship requires calculus methods and involves a differential equation. For continuously varying charge the current is defined by a derivative

包含电池、电阻和电容的电路的瞬态行为由欧姆定律、电压定律和电容的定义所支配。发展电容器充电关系需要微积分方法，并涉及一个微分方程。对于连续变化的电荷，电流由导数定义。

This kind of differential equation has a general solution of the form:

这种微分方程的通解形式为：

and the detailed solution is formed by substitution of the general solution and forcing it to fit the boundary conditions of this problem. The result is

该详细解是通过将通解代入并使其满足该问题的边界条件而得到的。结果是

Charging capacitor

给电容器充电

Capacitor discharge

电容器放电

Index

DC Circuits

Capacitor Concepts

索引直流电路电容器概念

HyperPhysics***** Electricity and Magnetism

HyperPhysics ***** 电学和磁学

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Capacitor Discharge Calculation

电容器放电计算

For circuit parameters:

R = Ω, V₀ = V

C = μF, RC = s = time constant.

C = μF, RC = s = 时间常数。

中文译文中的待填/计算数值依次对应：1：cc 2：rc。实际数值以上方原输入框为准。

This circuit will have a maximum current of I_max = A
这个电路的最大电流为 I max = A
中文译文中的待填/计算数值依次对应：1：im。实际数值以上方原输入框为准。
just after the switch is closed.

The charge will start at its maximum value Q_max= μC.
电荷将从最大值开始，Q max = μC。
中文译文中的待填/计算数值依次对应：1：qm。实际数值以上方原输入框为准。

At time t = s= RC
在时间 t = s= RC
中文译文中的待填/计算数值依次对应：1：t 2：trc。实际数值以上方原输入框为准。

the current is = I_max = A,
电流是 = I max = A,
中文译文中的待填/计算数值依次对应：1：i 2：ia。实际数值以上方原输入框为准。

the capacitor voltage is = V₀ = V,
电容器电压是 = V₀ = V，
中文译文中的待填/计算数值依次对应：1：vcf 2：vc。实际数值以上方原输入框为准。

and the charge on the capacitor is = Q_max = μC
电容器上的电荷为 Q max = μC
中文译文中的待填/计算数值依次对应：1：q 2：qa。实际数值以上方原输入框为准。

开关闭合后的瞬间

Capacitor discharge derivation

电容器放电推导

Capacitor charging discussion

电容器充电讨论