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A fuel gauge uses a capacitor to determine the height of
Chapter 24, Problem 74P(choose chapter or problem)
A fuel gauge uses a capacitor to determine the height of the fuel in a tank. The effective dielectric constant keff changes from a value of 1 when the tank is empty to a value of K, the dielectric constant of the fuel, 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. Each of the two rectangular plates has a width w and a length L (Fig. P24.68). The height of the fuel between the plates is h. You can ignore any fringing effects. (a) Derive an expression for Keff as a function of h. (b) What is the effective dielectric constant for a tank if the fuel is gasoline (K = 1.95)? (c) Repeat part (b) for methanol (K = 33.0). (d) For which fuel is this fuel gauge more practical?
Questions & Answers
QUESTION:
A fuel gauge uses a capacitor to determine the height of the fuel in a tank. The effective dielectric constant keff changes from a value of 1 when the tank is empty to a value of K, the dielectric constant of the fuel, 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. Each of the two rectangular plates has a width w and a length L (Fig. P24.68). The height of the fuel between the plates is h. You can ignore any fringing effects. (a) Derive an expression for Keff as a function of h. (b) What is the effective dielectric constant for a tank if the fuel is gasoline (K = 1.95)? (c) Repeat part (b) for methanol (K = 33.0). (d) For which fuel is this fuel gauge more practical?
ANSWER:Solution 74P Let us copy the figure given in the question. This arrangement can be thought to consist of two capacitors, one is of air and the other of fuel. They are parallel to each other. The area of the fuel part A = hw 1 K 0 1 hwK A0 1 The capacitance of the fuel part C = 1 d = d The area of the air part A = 2L h)w A (Lh)w The capacitance of the air part C = 2 0 = 0 2 d d hwK 0 1 (Lh)w0 w 0 The equiv