Resistance

Why does thick copper wire have lower resistivity, i know electrons flow more easily, but isnt the equation p=RA/L
It should increase resistivity?

Reply 1

uberteknik

Original post by Zenarthra

Why does thick copper wire have lower resistivity, i know electrons flow more easily, but isnt the equation p=RA/L
It should increase resistivity?

the derived unit of resistivity is: ohm metre

equating dimensions for p=RA/L gives

ohm metre = ohm m²/m

ohm metre = ohm metre

i.e. Area/length = length

n'est-ce pas?

(edited 9 years ago)

Reply 2

Zenarthra

Original post by uberteknik

the derived unit of resistivity is: ohm metre

equating dimensions for p=RA/L gives

ohm metre = ohm m²/m

ohm metre = ohm metre

i.e. Area/length = length

n'est-ce pas?

But why does increasing area decrease resistivity?
I dont understand.
And no it isn't, not for me :biggrin:

Reply 3

uberteknik

When is your exam?

If it's today, you will be better off resting and relaxing and letting your mind subconsciously absorb what you have learned.

Last minute swatting will only stress you out, exhaust you and you won't perform your best in the exam.

Reply 4

uberteknik

Original post by Zenarthra

But why does increasing area decrease resistivity?
I dont understand.
And no it isn't, not for me :biggrin:

Relax, you are overthinking.

What is resistivity? It is a property of the material that alters the ratio between Voltage and Current.

i.e. R = V/I

If the c.s.a. of the conductor is increased but the voltage pressure forcing electrons through the conductor remains constant, then more electrons per unit volume can pass through the conductor for the same voltage pressure.

Think of it like how much water can flow under a bridge if the pressure pushing the water (force per unit area) remains constant but the river is now made much wider and much deeper. A huge volume of water will now flow.

Reply 5

Zenarthra

Original post by uberteknik

I understand what more water will flow if you have a wider tube.
But what i dont understand is the equation p=RA / L p is proportional to A isnt it?

Reply 6

uberteknik

Original post by Zenarthra

I understand what more water will flow if you have a wider tube.
But what i dont understand is the equation p=RA / L p is proportional to A isnt it?

Resistivity is a normalised value allowing one material to be compared with another.

If you simply knew the resistance of two materials, it would tell you nothing about their dimensions, thermal coefficients etc.

Resistivity is a constant for that material which can be used to calculate actual resistance of the bulk material if you know it's dimensions (and temperature but this is not discussed here).

Resistivity is analogous to say permittivity or permeability. It's a constant value for a given material which allows actual resistance to be calculated when you add in the variables of c.s.a, length and thermal coefficient.

Reply 7

Zenarthra

Original post by uberteknik

Thanks for all the help, got exam now bye. :biggrin:

Reply 8

Stonebridge

Original post by Zenarthra

Why does thick copper wire have lower resistivity, i know electrons flow more easily, but isnt the equation p=RA/L
It should increase resistivity?

It doesn't.

Resistivity is a property of the material. It doesn't change if you have a longer piece or a thicker piece. (Assuming no change in temperature.)

It's resistance that changes if you increase the length or cross section.

The defining formula for resistivity

R = \frac{\rho l}{A}

is telling you that if you take the same length L and cross section A of two different materials, the resistance will be different. It's the resistivity ρ in that formula that gives you the constant that shows this difference.

Rearranging a formula like this to

\rho = \frac{RA}{l}

and then asking how increasing A changes ρ, is missing a very important point. If you change A you also change R. Increase A and you reduce R. The result is they cancel out.

If you are asking why increasing A decreases resistance, just think for a moment, A single wire with cross section 2A will have half the resistance of a single wire with cross section A. Why? Because a single wire with cross section 2A behaves the same way as two wires with cross section A placed side by side. (Total cross section =2A) If the wires are side by side they are in parallel. What is the resistance of two identical wires, resistance R, placed in parallel?

Reply 9

CajunCrab

Original post by Zenarthra

Why does thick copper wire have lower resistivity, i know electrons flow more easily, but isnt the equation p=RA/L
It should increase resistivity?

If you rearrange the equation it will show that resistance is proportional to 1/A, however thats just an equation.
Imagine a voltage (push) across a piece of copper, and that the free electrons are in rows being pushed, the more rows that you have all with the same push means more electrons moving which is more current for the same push so the resistance must be lower.