A copper wire and an iron wire - Potential difference

[mk9898]

Homework Statement

A copper wire and an iron wire of equal length l and diameter d are joined, and a potential difference V is applied between the ends of the composite wire. Calculate the potential difference (in volts) across the iron wire. Assume that l = 2.00 m., d = 0.30 mm., and V = 156 V.

The Attempt at a Solution

156 * 10 / (10+1.7) = 133.33 volts

156 * 1.7 / (10+1.7) = 22.67 volts

My question is: where do these equations come from? What are the derivations?

Thanks in advance.

 

[Lazar Lakic]

How did you come up with with your solution attempt and what are your thoughts behind it ?

 

[mk9898]

I should have noted that the solution and question in and of itself I found while searching google. I just want to know how they came about this solution i.e. where did this equation come from.

 

[Lazar Lakic]

Ah... I think its a remix of Ohm law, V=RI , where they have rewritten the resistance as L/(σ*A) , where σ is the conductivity of a given material.

I not entirely sure tho, some units on the calculations would have helped a lot hehe

 

[mk9898]

I not entirely sure tho, some units on the calculations would have helped a lot hehe

Yea exactly what I thought. In general it is: $\Delta V_1 = \frac{\Delta V * R_1}{R_1+R_2}$. I tried to work backwards having the denominator on the other side but still not sure what it could be. I then thought it has something to do with resistors in parallel but this exercise comes from a chapter before DC circuits are introduced.

 

[Lazar Lakic]

On the right track , try to Calculate R_copper and R_Iron and the current separately.
I think you are supposed to find the conductivity of Iron and copper in your book as they are not stated in the problem.

 

[mk9898]

I got it. It has to do with the Kirchhoff's Voltage Law. Here is a website explaining it:

http://www.solved-problems.com/circuits/circuits-articles/482/voltage-divider-voltage-division-rule/

Though I do find it odd that such an exercise comes before KVL is even introduced.