Use the following constants if necessary. Coulomb constant, k = 8.987 × 10º N · m²/C² . Vacuum permitivity, €o = 8.854 × 10-12 F/m. Magnitude of the Charge of one electron, e = –1.60217662 × 10¬19 C. Mass of one electron, me = 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 kchanges 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 = 19 cm, length L = 12 cm and breadth d = 18 cm. The height of the fuel between the plates is h = 7 cm. A battery with e.m.f of 12 v is connected across the plates. For gasoline, dielectric constant K, 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?
Use the following constants if necessary. Coulomb constant, k = 8.987 × 10º N · m²/C² . Vacuum permitivity, €o = 8.854 × 10-12 F/m. Magnitude of the Charge of one electron, e = –1.60217662 × 10¬19 C. Mass of one electron, me = 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 kchanges 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 = 19 cm, length L = 12 cm and breadth d = 18 cm. The height of the fuel between the plates is h = 7 cm. A battery with e.m.f of 12 v is connected across the plates. For gasoline, dielectric constant K, 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?
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Transcribed Image Text:Use the following constants if necessary. Coulomb constant, k = 8.987 × 10º N · m²/C² . Vacuum permitivity, €o = 8.854 × 10-12 F/m. Magnitude
of the Charge of one electron, e = –1.60217662 × 10¬19 C. Mass of one electron, me = 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 kchanges 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 = 19 cm, length L = 12 cm and breadth d = 18 cm. The height of the
fuel between the plates is h = 7 cm. A battery with e.m.f of 12 v is connected across the plates. For gasoline, dielectric constant K, 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?
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