# Quick question on resistance&current in a sheet

1. Sep 6, 2010

### vorcil

1. The problem statement, all variables and given/known data

A sheet of copper 0.6m in total length and 0.2m wide is folded to create a uniform spacing of 1mm.
the sheet is 1mm thick. a potential difference of 1mV is applied at the open end in such a way that the current is distrubuted unformly over the cross sectional area of the metal.
I can neglect the effects of the fold (the vertical bit)

http://yfrog.com/f/5mpicbvwp/
(i also forgot to draw in the battery, connecting the two ends of the open side, it has a potential difference of 1mV)

Find the resistance of the sheet,
and the current.

2. Relevant equations

https://secure.wikimedia.org/wikipedia/en/wiki/Sheet_resistance

In griffiths, I do not see this formula anywhere, however I'm going to use it anyway.

properties of copper:
electrical resistivity: 1.7*10^-8 ohms per metre
density: 8.9*10^3 kg m^-3
atomic weight = 64amu

3. The attempt at a solution

$$R = \rho \frac{L}{A} \Rightarrow A = 0.2m * 1mm$$

the length of the sheet is 0.6m

plugging in the values

$$R = (1.7*10^-8) * \frac{0.6}{0.2(1*10^-3)} = (5.1*10^-5) =51micro ohms$$

-

finding the current through the sheet, i'm just going to use Ohm's law,
$$\mathbf{J} = \sigma\mathbf{E} \Rightarrow \mathbf{V=IR}$$

plugging in the values, 1mV and 51 micro ohms, I get 19.6 Amps,
however I don't know if I'm right, because that seems superlarge to me?
where have I gone wrong???

-> can I not use the formula on this page? https://secure.wikimedia.org/wikipedia/en/wiki/Sheet_resistance