Question

A capacitive level sensor has the dimensions and properties shown below. What is the capacitance C in picofarads at the liquid level shown? Type in a one-decimal number

H = 4.0 meters

h = 3.9 meters

a = 1.0 millimeters

b = 6.0 millimeters

ε = 8.8542 x 10 picofarads/meter

k = 78.5

Answer 1

Since no image is attached, we can only guess that H and h are the dimensions of the plates, assume a is the plate separation, and k is the dielectric constant of the liquid. If b is the level of liquid, we have a configuration of two capacitors connected in parallel with the equivalent capacitance

$$C=\frac{\epsilon_oH(h-b)}{a}+\frac{k\epsilon_oHb}{a}=\\\space\\ =\frac{\epsilon_0H}{a}(h-b(1-k)).$$