# 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