Use the following constants if necessary. Coulomb constant, k = 8.987 x 10° N - m²/C2. Vacuum permitivity, €o = 8.854 x 10 12 F/m. Magnitude of the Charge of one electron, e =-1.60217662 x 10 19 C. Mass of one electron, m, = 9.10938356 x 10 31 kg. Unless specified otherwise, each symbol carries their usual meaning. For example, µC means micro coulomb. Battery Air Fuel
A fuel gauge uses a capacitor to determine the height of the fuel in a tank. The effective dielectric constant κchanges from a value of 1 when the tank is empty, to a value of 7, when the tank is full. The appropriate electronic circuitry can determine the effective dielectric constant of the combined air and fuel between the capacitor plates. The dimension of the fuel tank is width w=19cm, length L=12cm and breadth d=18cm. The height of the fuel between the plates is h=7cm. A battery with e.m.f of 11v is connected across the plates. For gasoline, dielectric constant κg You can ignore any fringing effects.
a) Calculate the effective dielectric constant of the fuel tank. (Hint: Consider two different capacitors connected in parallel)
b) How much energy is stored in the fuel tank when it is full up by gasoline?
c) What is the capacitance, when 0.75 fraction of the fuel tank is filled by the gasoline?
d) What is the capacitance, when the fuel tank is totally filled by the gasoline?
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