My Unanswered Question

[Apteronotus]

Hi,

I've asked this one question in one form or another a couple of times now and no one seems to have a good idea as to how to solve it. So I'll ask it again, in the hopes that the right person may come across it.

Suppose you have a simple capacitor, where the potential on one side is held constant and the other varies randomly.

What is the capacitive current?


thanks,

[Bob S]

Use the relation Q=CV, where Q is the charge, C = capacitance, and V = voltage across the capacitor. Now differentiate, yielding

dQ/dt = I = C dV/dt

Bob S

[Apteronotus]

Hi Bob, Thank you for your reply.

The problem is that since V is a random function, its derivative is not defined, (to my knowledge).

[berkeman]

Hi Bob, Thank you for your reply.

The problem is that since V is a random function, its derivative is not defined, (to my knowledge).

I'm not sure what kind of answer you want. Do you understand the relationship between the voltage on a capacitor and the current flowing through the capacitor? It's a direct relationship. Just because you only have a random representation for the voltage, that doesn't change the fundamental capacitor equations.

What is the context of your question? What is the physical setup? Maybe that will help us understand why you are asking this.

[Apteronotus]

I'm not sure what kind of answer you want. Do you understand the relationship between the voltage on a capacitor and the current flowing through the capacitor? It's a direct relationship. Just because you only have a random representation for the voltage, that doesn't change the fundamental capacitor equations.

What is the context of your question? What is the physical setup? Maybe that will help us understand why you are asking this.

Hi,
So perhaps I should make myself more clear. Though I have no background in physics, I do understand the relationship \left(I_C=C\frac{dV}{dt}\right) between voltage on a capacitor and the current flowing through the capacitor.

What I dont understand is, given that V is random with some distribution, how do you calculate this equation?
It seems that to calculate, one would have to take the derivative of a random signal, V. To my knowledge this is not possible.

To put it another way, if all we know is that V~N(0,1) then what is \left(\frac{dV}{dt}\right)?

The context is the current across a biological cell, due to a voltage gradient across the cell membrane. Some of the current will pass through the cell membrane, some will cause a build up of charge on the cell. What are the equations describing this when the voltage gradient is noise? (Before, I tried to keep my question as general as possible, so that other forum members could also benefit, but this is the context of my question)

Thanks

[berkeman]

Ah, much more clear now,thanks. THe random voltage fluctuations will have a finite bandwidth, which makes them differentiable. Does that help? I'm not real strong on differentiations of random functions, but I'm pretty sure that you can do it after you define the bandwidth characteristics of the random voltage signal.

[LeadDreamer]

Your biggest problem is trying to state "varying randomly", while accepting the relationship between voltage and current on a capacitor. In particular, **WHY** would the voltage be "randomly"? If what you are seeing is that you MEASURE it "varying randomly", then something must be CAUSING it to do so. What you CAN then say is that you KNOW the current flowing into/out of the capacitor follows the relationship above. Absent something CAUSING the changes (i.e. injecting current into/out of the capacitor), the voltage would be steady - and related to the charge on the Cap.

[berkeman]

Your biggest problem is trying to state "varying randomly", while accepting the relationship between voltage and current on a capacitor. In particular, **WHY** would the voltage be "randomly"? If what you are seeing is that you MEASURE it "varying randomly", then something must be CAUSING it to do so. What you CAN then say is that you KNOW the current flowing into/out of the capacitor follows the relationship above. Absent something CAUSING the changes (i.e. injecting current into/out of the capacitor), the voltage would be steady - and related to the charge on the Cap.

Welcome to the PF, LeadDreamer. Your style of posting is making me dizzy....