Resistance vs Current: I ∝ m/a^2

In summary, the participants in this conversation are discussing a mathematical relationship involving current, mass, and cross-sectional area. They touch upon the use of symbols like "ρ" and "d" in expressing this relationship, and the potential for confusion or ambiguity in using symbols interchangeably without proper context. They also mention the importance of considering factors like voltage and physical makeup of the conductor when discussing the relationship between current and resistance. Overall, it is important to be aware of the physical implications of mathematical manipulations in order to fully understand the underlying concepts being discussed.
  • #1
gracy
2,486
83
resistivity.png

Should not there be R (resistance) instead of I (current)in the last line i.e
I ∝ m/a^2
 
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  • #3
gracy said:
View attachment 82545
Should not there be R (resistance) instead of I (current)in the last line i.e
I ∝ m/a^2
If this is an electrical question, there's something missing from that final line...
 
  • #4
XZ923 said:
If this is an electrical question,
Yes,It is.
 
  • #5
XZ923 said:
there's something missing from that final line...
What's that?
 
  • #6
gracy said:
What's that?
The answer is actually very similar to the one I posted in your previous thread...

I'm trying not to just give it away. Here's a hint: review Ohm's Law
 
  • #7
It is a "proportional to" sign in the last line. It is a weird way to express the proportionality, however.
 
  • #8
mfb said:
It is a "proportional to" sign in the last line. It is a weird way to express the proportionality, however.

Very true; I'm just not a fan of expressing a current-to-resistance proportionality without a requirement that "voltage remains constant".

To better answer the OP's question:
Assuming voltage remains constant, resistance and current are inversely proportional to each other
Assuming the physical makeup of the conductor remains the same, cross-sectional area an resistance are inversely proportional to each other
Therefore, assuming voltage and physical makeup of the conductor remain the same, current and cross-sectional area of the conductor are directly proportional
 
  • #9
There's something I am not getting about the OP. The symbol ρ is commonly used for Resistivity and also for Density. It strikes me that the two appear to be used interchangeably in the attachment. I don't see the logic of the argument being used in that attachment. Can someone explain. please?
 
  • #10
Maybe she can provide more context. Is that from the internet?
Without context looks like a bizarre relationship.

They seem to use d for density and ρ for resistivity.
 
  • #11
@gracy
It is often possible to take two unrelated expressions, then re-arrange them, algebraically, assume that some of the variables in each expression are the same value and get an unexpected apparent relationship between two variables. It can be mathematically correct but of no meaningfulness in terms of the Physics at work. One needs always to be aware of the physical implications of such bits of maths manipulation.
 

What is the relationship between resistance and current?

The relationship between resistance and current is described by Ohm's Law, which states that current is directly proportional to voltage and inversely proportional to resistance. In other words, as resistance increases, current decreases, and vice versa.

What does the equation I ∝ m/a^2 mean?

The equation I ∝ m/a^2 represents the relationship between current (I) and resistance (m/a^2). This means that as resistance increases (m/a^2), current decreases (I). It also implies that current is directly proportional to the inverse of resistance (1/m) squared.

How does resistance affect current?

Resistance affects current by impeding the flow of electrons through a circuit. The higher the resistance, the harder it is for electrons to flow, resulting in a lower current. Conversely, lower resistance allows for easier flow of electrons and results in a higher current.

What is the unit of measurement for resistance and current?

The unit of measurement for resistance is the ohm (Ω), named after German physicist Georg Ohm. The unit of measurement for current is the ampere (A), named after French physicist André-Marie Ampère.

Is the relationship between resistance and current always linear?

No, the relationship between resistance and current is not always linear. It follows Ohm's Law in most cases, but there are materials and circuits where this relationship is not linear. In these cases, the relationship may be described by other equations such as power laws or exponential functions.

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