# Capacitance and Resistance of a fluid

by TFM
Tags: capacitance, fluid, resistance
 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 $$C = \frac{\epsilon_0A}{d}$$ $$R = \frac{\rho l}{A}$$ 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
 Mentor P: 11,911 You're almost there. What does the "p" in pF mean? Hint: it's not 10-6.
 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
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
 Mentor P: 11,911 Yes, that looks good.
 P: 1,031 Excellent Thanks for your Assistance, Redbelly98, Most Appreciated TFM

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