Physical meaning of time-integral of voltage

In summary: Hi, thanks for replying. I am measuring voltage signals from electrodes in a plant to see if there is any change in voltage when objects are brought close to the electrode.So the voltage is just due to the proximity of the object to the electrode?In summary, the time integral of voltage may be useful for measuring statistical properties like deviation and so on.
  • #1
dom_stb
6
0
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.
 
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  • #2
If you divide the definite integral = area under the graph by the time interval you will get the average value.

[tex]{V_{average}} = {\textstyle{{\int {V(t)dt} } \over {\int {dt} }}}[/tex]

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.
 
  • #3
And the Standard deviation is actually the RMS value of the AC component.
 
  • #4
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.
 
  • #5
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.
 
  • #6
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.
 
  • #7
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?.
 
  • #8
The voltage i am measuring is just that; the electric potential of the electrode wrt ground - there is no transducer, just a voltage amplifier.
 
  • #9
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.
 

1. What is the physical meaning of the time-integral of voltage?

The time-integral of voltage is a measure of the total electrical energy received by a circuit over a period of time. It represents the accumulated voltage over time and is typically measured in units of volts-second (V*s).

2. How is the time-integral of voltage calculated?

The time-integral of voltage can be calculated by taking the area under the voltage-time curve on a graph. This can be done manually by finding the area of each individual rectangle, or it can be calculated using mathematical integration techniques.

3. What is the significance of the time-integral of voltage in circuit analysis?

The time-integral of voltage is an important concept in circuit analysis as it allows us to understand the total energy consumption and storage within a circuit. It can also help us to calculate the power and energy dissipation in a circuit.

4. How does the time-integral of voltage relate to the concept of charge?

The time-integral of voltage is closely related to the concept of charge, as it is essentially the product of voltage and time. This means that the time-integral of voltage is directly proportional to the charge accumulated in a circuit over time.

5. Can the time-integral of voltage have negative values?

Yes, the time-integral of voltage can have negative values. This occurs when the voltage in a circuit is negative for a period of time, resulting in a negative area under the voltage-time curve. This can happen, for example, when a capacitor is discharged in a circuit.

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