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# Question: The ligure shows metal fuel lank in lhe shape of rectangular prism: its base is square wilh side and height is h. At small dislance d from one side is rec...

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###### Question: The ligure shows metal fuel lank in lhe shape of rectangular prism: its base is square wilh side and height is h. At small dislance d from one side is reclangular metal plate, dimensions h. It is red in the sketch and is almost touching the floor and the walls of the tank The sketches are not to scale (in fact; d < < so that the plate and the tank when empty; constitute simple parallel plate capacitor with dimensions by h and separation d, where edge effects may be neglected. Cap

Question: The ligure shows metal fuel lank in lhe shape of rectangular prism: its base is square wilh side and height is h. At small dislance d from one side is reclangular metal plate, dimensions h. It is red in the sketch and is almost touching the floor and the walls of the tank The sketches are not to scale (in fact; d < < so that the plate and the tank when empty; constitute simple parallel plate capacitor with dimensions by h and separation d, where edge effects may be neglected. Capillary effects are also negligible: The second sketch shows the tank with depth y of fuel which nas dielectric constant (Greek kappa not k); Our plan is to use the capacitance between plate and tank as fuel gauge . (Hint we can treat partly filled capacitor as two capacitors. Tank Fuel Figure The eft figure depicts an empty fuel tank: Ithas square base, side and height h capacitor plate size approximately by h, is parallel t0 one wall, which is the other capacitor plale, at distance away: Right figure depicts the fuel tank now partially filled with fuel (yellow) up to height y: This Ills Ihe capacitor to height y: Part 1) In terms of the variables named and any relevant constants derive an expression for the capacitance between the plate and the tank when the fuel reaches height y as shown Part 2) Hence derive an expression for the sensitivity of this fuel gauge, capacitor IS negligible compared with that in the tank where V is the volume of fuel in tne tank (Remember that d < < So the volume of fuel in the Part 3) Consider tank with side a = 63 cm; ad height h = 15 cm_ with capacitance spacing d = 1.0 mm and containing korosene with k 1.8. Express tho sensitivity of the gauge in picofarads per litre dv pF /litre

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