Resistance vs Current: I ∝ m/a^2

[gracy]

Should not there be R (resistance) instead of I (current)in the last line i.e
I ∝ m/a^2

 

[mfb]

Probably.

 

[XZ923]

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...

 

[gracy]

If this is an electrical question,

Yes,It is.

 

[gracy]

there's something missing from that final line...

What's that?

 

[XZ923]

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

 

[mfb]

It is a "proportional to" sign in the last line. It is a weird way to express the proportionality, however.

 

[XZ923]

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

 

[sophiecentaur]

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?

 

[nasu]

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.

 

[sophiecentaur]

@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.