Estimate the Resistance of a Gold Wedding Ring

[Dhooy7]

Homework Statement

Estimate the resistance of a gold (wedding-type) ring. State clearly all assumptions, and introduce any equations you use. your solution should also include a brief summary of how you approached and solved the problem. Helpful tip:

You will have to make certain assumptions. My professor is not looking for one particular numerical answer. Any reasonable approximations will be acceptable.

Homework Equations

I have the Resistance equation.

The Attempt at a Solution

We have to make assumptions. I would need to lookup the resistivity of gold.

Not sure though how to do it though if it is 50% copper as well. If it was 100% gold, you would lookup the resistivity of gold, the length of gold ring (L), and figure out the area.

I would make an assumption for the radius. This would be a cross-sectional area I believe. I'm not really sure what some reasonable L, and R values are.

Also, what would you say about being 100% gold vs 50% copper and 50% gold?[/B]

 

[AdityaDev]

There is nothing wrong with assuming that the ring is pure gold.
The radius of cross section is important.

if r is the radius of cross section, then $\pi r^2$ is A.
Then you can find L when radius of ring is R.
You can then find R using the expression $R=\rho L/A$

So if you find R using the above method,the assumptions you would be making are:
1)the cross section of ring is circular
2)the ring is pure gold

 

[CWatters]

Many wedding rings are virtually flat strips formed into a circle. Perhaps approximate to a rectangular cross section. This one about 6mm * 2mm...
http://www.bluenile.com/uk/low-dome-comfort-fit-wedding-ring-yellow-gold-18k_8045?click_id=501226522

Then two strips in parallel each having a length equal to half the circumference.

 

[Dhooy7]

What are some reasonable assumptions and values for a cross-sectional radius of a ring?

Is 0.1cm for r and what is the L for?

 

[AdityaDev]

The problem is, it is difficult to measure its resistance using circuits. For example, if you use a battery of 3V and an ammeter, then you have to connect the ring like this -()-. Now the equvivalent resistance depends on the arc length between the connecting wires. Once you know the equvivalent resistance in terms of R, use ammeter and baterry to find equivalent resistance from circuit and then equate the two. The value of R will not be precise.

 

[AdityaDev]

Here is a better assumption. After going through the dimensions of some wedding rings, I found that they almost have a semi circular cross section. 1.5mm radius is good.
so take radius of cross section as 1.5mm and assume semicircular cross section. The diameter can be taken from 15mm to 20mm.