# Capacitance and Resistance of a fluid

1. Dec 11, 2008

### TFM

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

A parallel plate air-spaced capacitor has a capacitance of 100pF. It is immersed in a fluid of resistivity 10 m. Calculate the resistance between the plates.

2. Relevant equations

$$C = \frac{\epsilon_0A}{d}$$

$$R = \frac{\rho l}{A}$$

3. The attempt at a solution

I seemed to get this question too easily...

First of all, I said that for the fluid, the area is the area of the pates, and l is the distance d between them, then I rearranged the resistivity equation into terms of a/d:

$$\frac{A}{d} = \frac{\rho}{R}$$

then I substituted this equation into the capacitance equation:

$$C = \epsilon_0\frac{\rho}{R}$$

rearrange for R:

$$R = \epsilon_0 \frac{\rho}{C}$$

Insert values:

$$R = \epsilon_0 \frac{10}{100*10^{-6}}$$

this gives a value of $$8.85 * 10^{-7}$$ Ohms

Does this look correct?

TFM

2. Dec 11, 2008

### Redbelly98

Staff Emeritus
You're almost there. What does the "p" in pF mean? Hint: it's not 10-6.

3. Dec 12, 2008

### TFM

pF is a pico Farad, I believe

Iyt is 10^-12, not -6, that was illy of me - I should have remebered that 10^-6 is micro

TFM

4. Dec 12, 2008

### TFM

Putting in my new value for C, I get the resistance to be:

0.885 Ohms

Does this look right now?

TFM

5. Dec 12, 2008

### Redbelly98

Staff Emeritus
Yes, that looks good.

6. Dec 13, 2008

### TFM

Excellent

Thanks for your Assistance, Redbelly98, Most Appreciated

TFM