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Capacitance and Resistance of a fluid

by TFM
Tags: capacitance, fluid, resistance
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TFM
#1
Dec11-08, 02:48 PM
P: 1,031
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

[tex] C = \frac{\epsilon_0A}{d} [/tex]

[tex] R = \frac{\rho l}{A} [/tex]

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:

[tex] \frac{A}{d} = \frac{\rho}{R} [/tex]

then I substituted this equation into the capacitance equation:

[tex] C = \epsilon_0\frac{\rho}{R} [/tex]

rearrange for R:

[tex] R = \epsilon_0 \frac{\rho}{C} [/tex]

Insert values:

[tex] R = \epsilon_0 \frac{10}{100*10^{-6}} [/tex]

this gives a value of [tex] 8.85 * 10^{-7} [/tex] Ohms

Does this look correct?

TFM
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Redbelly98
#2
Dec11-08, 05:20 PM
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P: 12,069
You're almost there. What does the "p" in pF mean? Hint: it's not 10-6.
TFM
#3
Dec12-08, 05:58 AM
P: 1,031
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

TFM
#4
Dec12-08, 01:29 PM
P: 1,031
Capacitance and Resistance of a fluid

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

0.885 Ohms

Does this look right now?

TFM
Redbelly98
#5
Dec12-08, 05:16 PM
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P: 12,069
Yes, that looks good.
TFM
#6
Dec13-08, 03:34 AM
P: 1,031
Excellent

Thanks for your Assistance, Redbelly98, Most Appreciated

TFM


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