A simple fuel level gauge can use the dielectric constant of the fuel to indicat

Question

A simple fuel level gauge can use the dielectric constant of the fuel to indicate its level in a tank. Consider the schematic drawn in the figure where the two rectangular plates of the capacitor have a width w, and a length L. The height of the fuel between the plates is h. The effective dielectric constant, keff, changes form a value of 1 when the tank is empty, to the value of the dielectric constant of the fuel, k , when the tank is full. The appropriate electronic circuitry can determine the effective dielectric constant of the system. a) Ignoring any fringe effects, derive an expression for the keff as a function of h. b) What is the dielectric constant for a tank that is

Explanation / Answer

a)

Ceff = C1 + C2

keff L w = 1 * (L-h) w + k * h w

keff = (L-h)/L+ k h/L

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part (b):

1/2 full:

keff = (L-h)/L+ k h/L = (1-1/2)/1+ 1.95* (1/2)/1 = 1.475

3/4 full:

keff = (L-h)/L+ k h/L = (1-3/4)/1+ 1.95* (3/4)/1 = 1.7125

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c)

1/2 full:

keff = (L-h)/L+ k h/L = (1-1/2)/1+ 33* (1/2)/1 = 17

3/4 full:

keff = (L-h)/L+ k h/L = (1-3/4)/1+ 33* (3/4)/1 = 25

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d)

methanol, because Keff is in a wide range for methanol.

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