A fuel gauge uses a capacitor to determine the height of thefuel in a tank. The

Question

A fuel gauge uses a capacitor to determine the height of thefuel in a tank. The effective dielecttric constant kchanges from a value of 1 when the tank is empty to a value of Kthe dielectiric constant of the fuel when the tank is full. The appropriate electronic circuitry can determine the effectivedielectric constant of the combined ait and fuel between thecapacitor plates. Each of the two rectangular plates has awidth w and a length L. The height of the fuel between theplates is h. You can ignore any fringing effects. a) Derive an expression for k as a function of h b) What is the effective dielectric constant for a tank (1/4)full, (1/2) full, and (3/4) full if the fuel is gasoline(K=1.95) c) Repeat part b for methanol (k=33) d) For which fuel is this fuel gauge more practical A fuel gauge uses a capacitor to determine the height of thefuel in a tank. The effective dielecttric constant kchanges from a value of 1 when the tank is empty to a value of Kthe dielectiric constant of the fuel when the tank is full. The appropriate electronic circuitry can determine the effectivedielectric constant of the combined ait and fuel between thecapacitor plates. Each of the two rectangular plates has awidth w and a length L. The height of the fuel between theplates is h. You can ignore any fringing effects. a) Derive an expression for k as a function of h b) What is the effective dielectric constant for a tank (1/4)full, (1/2) full, and (3/4) full if the fuel is gasoline(K=1.95) c) Repeat part b for methanol (k=33) d) For which fuel is this fuel gauge more practical

Explanation / Answer

The dielectrics will add in proportion to their heights, so weneed to add the height of the gas times K plus m - that heighttimes the dielectric of air, which is 1.
k = (h/m) K + (1 - h/m) (1)
For K - 1.95, here are the effective dielectricconstants:
h = 0.25: K =.75 + .25 * 1.95 = 1.238 h = 0.5: K = .5 + .5 * 1.95 = 1.475 h = 0.75: K = .25 + .75 * 1.95 = 1.713
for k = 33, these become:
h = 0.25: K =.75 + .25 * 33 = 9 h = 0.5: K = .5 + .5 * 33 = 17 h = 0.75: K = .25 + .75 * 33 = 25
The second case (methanol) is much more sensitive and thusmore practical h = 0.25: K =.75 + .25 * 33 = 9 h = 0.5: K = .5 + .5 * 33 = 17 h = 0.75: K = .25 + .75 * 33 = 25
The second case (methanol) is much more sensitive and thusmore practical

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