CR电路[CR Circuit] - 达人(其实～我是卧底，来自外星)

2005/03/20 | CR电路[CR Circuit]
类别(Ω〖物理〗) | 评论(1) | 阅读(184) | 发表于 13:33: Given an electric circuit composed of a resistor with resistance R and a capacitor with capacitance C, the Kirchhoff loop rule requires that the sum of the changes in potential must be zero, so
(1)

where I is the current through the resistor and Q is the charge on the capacitor. Differentiating,
(2)

and rearranging gives
(3)

which is a first order ordinary differential equation with solution

Here, is the current at time t = 0 and is a decay constant defined by
(4)

For a sinusoidally driven CR circuit, use the equation of a sinusoidally driven CLR circuit with L = 0
(5)

where the phase lag is
(6)

so the current leads the voltage. The complete solution is then
(7)

where is the permittivity of free space.; 0