# Resistivity of a current in a fluid

1. Oct 8, 2012

### hsetennis

I am studying the resistivity of various materials in my physics class and I have a query regarding conductive fluids.

If a current is running through a fluid (let's say water) within a rectangular beaker, and there are two copper wires put in at opposite ends of a beaker (I believe they are called electrodes?).

Supposing I connect the multimeter/ohmmeter to the wires outside of the beaker, I should get a reading in ohms. Now to find the resistivity of the fluid at that Â°C/Pa, I would solve by using $\rho=\frac{(Resitivity)(Length}{Cross-Sectional Area}$. I assume the length would just be the distance between electrodes, but I don't know if the area is the whole area of the beaker. Can someone shed light on this?

*I don't want to call it an electrolytic cell, because I'm using very small amps/volts.
*Also, this isn't a homework/coursework question. I'm just curious about it and my teacher was unsure. Pardon me if it's in the wrong section

Thanks.

2. Oct 9, 2012

### Naty1

More ions in a conducting liquid will take a shorter rather than a longer path because the resistance is less along the shorter path. If you use a larger beaker likely the resistivity you measure will be SLIGHTLY smaller.

This is analogous to hooking up wires of different lengths in parallel: most current will flow thorugh the shortest wire, the least current will flow thru the longest wire.

3. Oct 9, 2012

### Studiot

Firstly we generally measure the inverse of resistivity ie conductivity of a conductive fluid.

Secondly the conductivity is independent of the volume of the fluid.

People with aquaria and swimming pools know this and use conductivity meters to dip into their tanks. These work the same regardless of tank size. Water scientists use these meters to measure the water quality of natural waters (ponds, rivers etc).

Please note for resistivity /resistance and conductivity / conductance both pairs refer to different properties.

The resisitivity or conductivity is a bulk material property and independent of the distance between the electrodes for any state of matter, solid, liquid or gas.

The resistance, on the other hand depends upon the quantity and disposition (length and cross section) as well as the resistivity.