I'm interested in calculating the(adsbygoogle = window.adsbygoogle || []).push({}); capacitive currentwhen the electric field across a capacitor is given by a random function. The randomness of the electric field deems the usual [tex]I_c=C\frac{dV}{dt}[/tex] useless; since the derivative of a random function [tex]V[/tex] cannot be calculated.

To approach the problem in another way, I'd like to calculate the charge [tex]q(t)[/tex] on a capacitor in an RC circuit when the emf is given by a step function:

[tex]V(t)=V_1[/tex] for [tex]t\in(0,t_1)[/tex]

[tex]V(t)=V_2[/tex] for [tex]t\in(t_1,t_2)[/tex]

and

[tex]V(t)=V_3[/tex] for [tex]t\in(t_2,t_3)[/tex]

where

[tex]V_1<V_3<V_2[/tex]

I've calculated the charge [tex]q(t)[/tex] for [tex]t\in(t_1,t_2)[/tex] to be

[tex]q(t)=q_1+C(V_2-V1)(1-e^{\frac{t_1-t}{RC}})[/tex]

but am having a difficult time deriving the charge in the interval [tex](t_2,t_3)[/tex].

If anyone can help me with either of the problems I'd much appreciate it.

Thanks.

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# Dis/Charging capacitor in time varying electric field

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