(adsbygoogle = window.adsbygoogle || []).push({}); 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 thatfor 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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# Capacitance and Resistance of a fluid

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