Rank Resistances: A, B, C, A+B, B+C, A+B+C

[Firecloak]

Homework Statement

The figure below shows cross sections through three long square conductors of the same length and material, with square cross sections of edge lengths as shown. Conductor B fits snugly within conductor A, and conductor C fits snugly within conductor B.

Rank the following according to their end-to-end resistances, greatest first: the individual conductors and the combinations of A + B (B inside A), B + C (C inside B), and A + B + C (B inside A inside C).

http://img14.imageshack.us/img14/7955/phys2.jpg

Homework Equations

R = p (L/A)

The Attempt at a Solution

Each of them have a different length and area, so I don't know how to go about this problem.

 

[kuruman]

You have a relevant equation and the dimensions of your conductors. That's all you need.

 

[tomcue]

I would approach this problem by first identifying the key variables and equations that are relevant to calculating resistance. The key variables in this problem are length (L) and cross-sectional area (A) of the conductors. The equation for resistance (R) is R = p (L/A), where p is the resistivity of the material.

Next, I would consider the fact that the conductors are arranged in a series circuit, where the current flows through each conductor one after the other. In a series circuit, the total resistance is equal to the sum of individual resistances. Therefore, the end-to-end resistance of each combination can be calculated by adding the individual resistances of each conductor in the combination.

Now, let's look at the given figure and consider each combination separately:

1. Individual conductors: Conductor A has the greatest length and therefore, the greatest resistance. Conductor B has a shorter length than A, and C has the shortest length of all three. Therefore, the ranking of individual conductors based on end-to-end resistance would be A > B > C.

2. A + B (B inside A): In this combination, the current flows through B first and then through A. Since B has a shorter length than A, it would contribute less resistance compared to A. Therefore, the end-to-end resistance of this combination would be less than that of A alone, but greater than B alone. So the ranking would be B > A + B > A.

3. B + C (C inside B): In this combination, the current flows through C first and then through B. Similar to the previous combination, the shorter length of C would contribute less resistance compared to B. Therefore, the end-to-end resistance of this combination would be less than that of B alone, but greater than C alone. So the ranking would be C > B + C > B.

4. A + B + C (B inside A inside C): In this combination, the current flows through C first, then through B, and finally through A. Following the same logic as before, the end-to-end resistance of this combination would be less than that of A alone, but greater than B + C. So the ranking would be B + C > A + B + C > A.

Based on these rankings, the final ranking of all combinations and individual conductors from greatest to least end-to-end resistance would be: A + B + C