# Charging potential vs time graph.

• dE_logics
In summary, the conversation discusses the use of the symbol "tau" in graphs of capacitor charging/discharging, instead of the usual "t". This is because using "tau" as a unit of time allows for the graph to be scale invariant with respect to the values of resistance and capacitance. This is similar to using wavelengths as units of space in graphs of waves.

#### dE_logics

Why don't we simply take t as x? why is it t?

Where is the time constant.

If you're looking at a question mark instead of the symbol "tau"...you know its tau.

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dE_logics said:
Why don't we simply take t as x? why is it t?
You might get an answer if you explained what the question is.

AM

On one axis we have the charging current/voltage, while on the other instead of time (t) we have t ...why?

And yeah...latex is still giving problems?...I think I got a cache problem.

This picture shows what I'm seeing:

#### Attachments

• question.gif
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Actually I'm on linux, and so this website seems MS friendly.

So that 'tau' seems like a matrix in windows.

So if you encounter any sort of weird symbols, take it as 'tau' or time constant.

So are you trying to write $t / \tau$?

ITs t*tau not t/tau.

Latex just started working for me!

$$t \tau$$...this is what I mean.

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I've seen many capacitor charging/discharging graphs that use $t / \tau$ on one of the axes, but never one that uses $t \tau$. Are you sure the $\tau$ isn't a subscript, i.e. $t_{\tau}$?

Are you referring to graphs like this one?

The horizontal scale markings indicate $t = \tau$, $t = 2 \tau$, $t = 3 \tau$, etc. This means the same thing as $t / \tau = 1$, $t / \tau = 2$, $t / \tau = 3$, etc.

The 1, 2, 3, etc. are not t's. t and $\tau$ both have units of time, so the numbers are dimensionless.

Yeah...the same thing.

So why did this $$\tau$$ stuff pop by?...why not simply use time?

Normalization, the time constant will vary between different values of R and C but as long as you plot the time axis in terms of the time constant then the plots will all be the same (barring differences in the magnitude of the initial voltage).

Oh...you mean to maintain the nature of the graph...right?

Yeah. Plotting in units of time constants allows the graph to be scale invariant with respect to the R and C of the circuit. It's the same reason why when we plot graphs of waves and such we use wavelengths as our units of space. It automatically scales the plots in such a way that the information of interest is readily seen.

Humm...ok, thanks!

## What is a charging potential vs time graph?

A charging potential vs time graph is a graphical representation of the change in electrical potential over time during the charging process of a battery or capacitor. It shows how the potential difference between the two terminals of the device changes as it charges.

## What does a positive slope on a charging potential vs time graph indicate?

A positive slope on a charging potential vs time graph indicates that the potential difference is increasing over time, meaning that the battery or capacitor is charging. This indicates a flow of electrical current from the positive terminal to the negative terminal.

## What does a negative slope on a charging potential vs time graph indicate?

A negative slope on a charging potential vs time graph indicates that the potential difference is decreasing over time, meaning that the battery or capacitor is discharging. This indicates a flow of electrical current from the negative terminal to the positive terminal.

## What does a flat line on a charging potential vs time graph indicate?

A flat line on a charging potential vs time graph indicates that the potential difference remains constant over time, meaning that the battery or capacitor is fully charged and there is no flow of electrical current. This is also known as the saturation point.

## How can a charging potential vs time graph be used to determine the capacity of a battery or capacitor?

By analyzing the slope of the charging potential vs time graph, the capacity of a battery or capacitor can be determined. A steeper slope indicates a higher capacity, while a flatter slope indicates a lower capacity. The saturation point can also be used to determine the maximum capacity of the device.