Voltage vs Time Graph: Understanding & Deriving Relationships

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Discussion Overview

The discussion revolves around understanding and deriving relationships from a voltage vs. time graph, particularly in the context of a battery connected to a resistor. Participants explore how to interpret the graph and calculate charge over time, while clarifying the absence of capacitors in the scenario presented.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant asks about deriving charge from a voltage vs. time graph involving a battery and resistor.
  • Another participant suggests that the question may actually pertain to a capacitor, indicating a potential misunderstanding.
  • A different participant describes a specific graph scenario where voltage decreases linearly from 1.5V to 0V over three hours, questioning how to approach the problem without a capacitor.
  • One participant provides a formula for current based on the voltage and resistance, suggesting an integration approach to calculate charge, but questions the usefulness of the calculation.
  • Another participant calculates the slope of the voltage decrease and provides a linear equation for voltage over time.

Areas of Agreement / Disagreement

Participants express differing interpretations of the original question, with some focusing on the role of capacitors while others clarify the context of the battery and resistor. The discussion remains unresolved regarding the best approach to analyze the voltage vs. time graph.

Contextual Notes

Participants make assumptions about the linearity of voltage change and the nature of the circuit, which may affect their calculations and interpretations. There is also a lack of consensus on the relevance of the calculations provided.

megr_ftw
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What are you able to derive or integrate from a voltage vs. time graph? Like if I have a battery and a resistor and want to know the charge after so many hours or seconds.
We went over this in class but could someone elaborate the relationship?
 
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A battery across a resistor, voltage is constant, graph of voltage versus time is a horizontal straight line. Are you sure that your real question isn't about a capacitor?
 
I had a problem the teacher gave us and it was a graph of time(x-axis) vs. voltage(y-axis) and it had the line as a negative slope where the voltage of the battery was 1.5V and it crossed the y-axis at 3 hours. they gave us a resistor of x ohms.
So there is no capacitor in the problem and how should I treat it?

*note this is not a homework question, just a general one
 
You're question is a bit confusing... I'll try to help...
I'll assume:
-You're saying the battery's voltage is reducing linearly from 1.5V to 0V over a three hour duration.
-You're circuit is a battery with a resistor across it.
-You said something about charge, so I'll assume current.

Current, I=V/R

If you integrate that function, you get 0.5*(1.5V)/R*time. For example, let's assume that R=10 Ohms:
Then you could calculate: 0.5*1.5/10*3hr = 225mAh (milli amp hours).

But this is actually a useless calculation. Can you elaborate on your question?
 
elliotr said:
You're saying the battery's voltage is reducing linearly from 1.5V to 0V over a three hour duration.

I think the person needs:
decreasing 1.5 volts in 10800 seconds, for a slope of -0.0001389 volts per second
V = (-0.0001389 V/s) t + 1.5 V
 

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