Physical meaning of time-integral of voltage

[dom_stb]

Hello,

I have recorded voltage signals (in the time domain) using standard electrophys amplifiers. The voltage is that of an electrode inserted in a plant stem as charged objects are brought close to, then into contact with the flower.

I was wondering about the significance of the time integral of voltage: It is not clear to me what, if any physical significance this has.

Op-amp based voltage integraters in electronics measure the total electric flux through the amplifier - or so i understand it. Does this apply to the signals I measure?

I know if resistance is constant, voltage is proportional to current so the integration of V dt is proportional to charge, but without a reliable value for R this is useless to me.

I want to know exactly what quantity the integration of Vdt gives.
Any ideas?
Regards,
Dom.

 

[Studiot]

If you divide the definite integral = area under the graph by the time interval you will get the average value.

$${V_{average}} = {\textstyle{{\int {V(t)dt} } \over {\int {dt} }}}$$

You can use this to calculate various statistical properties such as the deviation and so on.

If you calculate the RMS value, rather than the average for both the voltage and current, their product gives the average power transferred during the time period.

 

[sophiecentaur]

And the Standard deviation is actually the RMS value of the AC component.

 

[dom_stb]

Hi, thanks guys.

So there is no direct physical meaning of the time-integral then? It is just a statistical tool.
I was wondering if there might be some quantity I could get out of it that would be a physical property in and of itself - like getting charge from the time-integral of current.

I read that integrating op-amps get total electric flux as they integrate the voltage on their inputs. I think this may just be something that is peculiar to a nice neat electronic system.

Measuring current in my particular application is appallingly difficult so i was hoping for something more out my voltage readings.

Thanks for replying though.

Dom.

 

[sophiecentaur]

That's a bit harsh on poor old time integral. The time integral can be very meaningful. It can tell you where you end up if you integrate velocity over time! Think Navigation.

 

[dom_stb]

Voltage-time integral though, not just any time integral.
It is because of the power of the time integral in general that i expected to be able to get something useful from my voltage-time data.

 

[sophiecentaur]

It depends upon what the Voltage you are measuring represents as to what its significance is, surely. Why are you measuring Volts in the first place? What is this Voltage due to? If it's position, then the average voltage is a measure of the average position. Is that of interest?.

 

[dom_stb]

The voltage i am measuring is just that; the electric potential of the electrode wrt ground - there is no transducer, just a voltage amplifier.

 

[sophiecentaur]

In that case, I would have to agree that the time integral (i.e. mean) voltage has no other interpretation than just that. Why should it have more significance? But your measurements are presumably 'for' something. Or is this varying voltage signal just something arbitrary on which to perform an analysis.
Or, perhaps, this is a question that you have been set which has no context known to you?
A totally mathematical problem may have no physical relevance.