# the dependence of (the) resistance on (the) temperature

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#### Alacer

##### Senior Member
Is the following phase correct?

...the dependence of resistance on the temperature reveals...

Thank in advance!

• #### the_del_star

##### Senior Member
I think dependency is necessary, instead of dependence.

*Is this for physics/chemistry?

#### Alacer

##### Senior Member
yes, for physics

#### Alacer

##### Senior Member
are you sure that "dependency" is more suitable? I always read "dependence", even in UK and USA scientific articles...

#### Alacer

##### Senior Member
I'm talking about the article "the". where is it necessary and where not?

#### the_del_star

##### Senior Member
I think it would be without the "the's"
"The dependence of resistance on temperature reveals"
I don't think there is a hard and fast rule for this, though.

#### nzfauna

##### Senior Member
What are the surrounding words/sentences? I think it depends on context.

#### Thomas Tompion

##### Senior Member
For me what we are probably talking about is a relationship, rather than a dependence. Doesn't dependence suggest that we are talking about the only important variable, that no others matter? This may be the case here, but are we sure?

A relationship between two things (x & y) can be:

direct: x up -> y up and vice versa

or

inverse: x up -> y down and vice versa.

Dependence by itself, for me, says nothing about whether the relationship is direct or inverse, just that there is only one variable that matters.

#### Alacer

##### Senior Member
For example, I'm saying "here you can see the dependence of resistance on temperature, that reveals...". I'm pointing at the slide where this graph of resistance versus temperature is shown.
This information can help, I think, to imagine the situation.

#### the_del_star

##### Senior Member
No, dependence does not mean that only one variable "matters"
It implies that the second variable (R) is a function of the temperature(t)

The graph would show R(t) where t is the written along the horizontal axis, and R along the vertical.

I had a go at my chem book, looking for similar phrasing of similar relationships, and I saw that the structure that uses "depends" was preferred over "dependence"
"As you can see the resistance depends on the temperature. This reveals... "

I think that this is just a matter of personal preference.

#### Thomas Tompion

##### Senior Member
No, dependence does not mean that only one variable "matters"
It implies that the second variable (R) is a function of the temperature(t)

The graph would show R(t) where t is the written along the horizontal axis, and R along the vertical.

I had a go at my chem book, looking for similar phrasing of similar relationships, and I saw that the structure that uses "depends" was preferred over "dependence"
"As you can see the resistance depends on the temperature. This reveals... "

I think that this is just a matter of personal preference.
You may be right about this TDS,

The problem, as I see it, is that, in simple functions, dependency does mean that the value of the one variable is dependent on the other, so, to my mind, saying that dependency doesn't mean that only one variable 'matters' but that one variable is a function of the other, seems misleading.

I probably didn't express myself very well when I used that word matter. Of course other factors, like the chemical composition of the material, will influence the shape of the graph of R against t.

In many functions, and maybe even here, as I was suggesting, there are many independent variables and to discover the relationship between individual ones and the dependent variable we have, surely, to hold all other relevant factors constant.

If we look at the phrase in question:

...the dependence of resistance on the temperature reveals...

1. The expression 'the dependence of resistance on the temperature' implies, I think that there is such a dependence, that R is a function of t.
2. That's fine, as I see it, as long as it doesn't close the possibility of R being a function of other things as well - something which is excluded, in my view, by the expression dependence, but not by the phrase R is a function of t.

This was the distinction I was, probably rather hamfistedly, trying to draw.

I'd prefer to see Alacer say the fact that resistance is a function of temperature reveals, unless he really means that there is only one effective independent variable.

#### the_del_star

##### Senior Member
I disagree that the expression dependence excludes R from being a function of any other variable, at least when I read it.

For example, PV=nRT. See here that the Pressure depends on the temperature. And it also depends on number of moles, AND volume. The relationship, even if the other unstated variables are not held constant, doesn't change. You can choose to examine any of these relationships, without excluding the others, in such a phrase.

Dependence is a little trickier than proportionality. It makes you define your perspective on how things are related. The amount of gas I buy at the pump depends on how much the gas costs, but the price of gas doesn't depend on how much I buy.
And, the amount of gas I buy also depends on how much further I plan on driving.

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#### Alacer

##### Senior Member
No, Thomas, that's not what I meant.
The dependence per se does interest the audience. I show them the graph, which is very complicated, with many sharp steps and linear parts. So, then I say that "this dependence of resistance on temperature reveals few steps which correspond to the phase transitions and the linear part which means the substance has metallic conductivity."
but that the resistance is a function of temperature is well know and is, of course, fact for everyone. they (audience) are interested in what this dependence includes and what conclusion can I draw looking at this complicated dependence.

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