Resistance, cross-sectional area of long coated wire

[Cocoleia]

Homework Statement

Homework Equations

The Attempt at a Solution

I attempted all of the parts:

I think I did the right things for a-b-c-d, but I am pretty unsure about e & f. Can someone verify if my logic is right? Thanks.

 

[haruspex]

think I did the right things for a-b-c-d

You have d wrong. The formula you quoted is not quite right.

 

[Cocoleia]

You have d wrong. The formula you quoted is not quite right.

Ah I see it should be 1/Req. If I change that, will the following steps be right assuming I use that value ?

 

[haruspex]

Ah I see it should be 1/Req. If I change that, will the following steps be right assuming I use that value ?

Your method in e) is right.
In f, you seem to have assumed all of I is in the inner wire when calculating the current density there.

 

[haruspex]

(a)-(d) look correct.
(e) is incorrect. You need to take the ratio as the question indicates, not the product.

If you read posts 2 and 3, you'll see that d) was wrong, and this led to the wrong expression in e.

 

[Cocoleia]

Your method in e) is right.
In f, you seem to have assumed all of I is in the inner wire when calculating the current density there.

How do I calculate it without assuming this? By the way, this isn't homework, I am just working on problems to prepare for an exam tomorrow.

 

[haruspex]

How do I calculate it without assuming this? By the way, this isn't homework, I am just working on problems to prepare for an exam tomorrow.

One way would be to suppose the potential applied to the wire is V and compute what current would flow in each component.