| Thread Closed |
Dis/Charging capacitor in time varying electric field |
Share Thread | Thread Tools |
| Jan11-10, 04:43 PM | #1 |
|
|
Dis/Charging capacitor in time varying electric field
I'm interested in calculating the capacitive current when 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. |
| Jan11-10, 04:48 PM | #2 |
|
Mentor
|
|
| Jan11-10, 05:25 PM | #3 |
|
|
Hi Berkeman,
Lets simply suppose we have an RC circuit connected to a voltage device (battery). For the first time interval [tex](0,t_1)[/tex] the battery voltage is [tex]V_1[/tex] for the second interval [tex](t_1,t_2)[/tex] the voltage is [tex]V_2[/tex] and so on... I want to measure the the amount of charge that would accumulate on the capacitor as a function of time. For the first time interval, we simply have [tex]q(t)=CV_1(1-e^{-\frac{t}{RC}})[/tex] for the second time interval we'd get [tex]q(t)=CV_1(1-e^{-\frac{t_1}{RC}}) + C(V_2-V_1)(1-e^{-\frac{t_1-t}{RC}})[/tex] now considering that [tex]V_3<V_2[/tex] the capacitor need to discharge slightly. So what is q(t) in the third time interval? Thanks. |
| Jan11-10, 05:36 PM | #4 |
|
Mentor
|
Dis/Charging capacitor in time varying electric field |
| Thread Closed |
| Thread Tools | |
Similar Threads for: Dis/Charging capacitor in time varying electric field
|
||||
| Thread | Forum | Replies | ||
| Magnetic Field and Poynting Flux in a Charging Capacitor | Introductory Physics Homework | 2 | ||
| Capacitor and Time Varying Potential | Introductory Physics Homework | 2 | ||
| The Magnetic Field in a Charging Capacitor | Advanced Physics Homework | 3 | ||
| Capacitor/Charging & magnetic Field | Advanced Physics Homework | 3 | ||
| A cylinder of electric field varying in time | Classical Physics | 5 | ||