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A tank containing a liquid has turns of wire wrapped around it, causing it to act like an inductor. The liquid content of the tank can be measured by using its inductance to determine the height of the liquid in the tank. The inductance of the tank changes from a value of Lo corresponding to a relative permeability of 1 when the tank is empty to a value of Lr corresponding to a relative permeability of Km (the relative permeability of the liquid) when the tank is full. The appropriate electronic circuitry can determine the inductance to five significant figures and thus the effective relative permeability of the combined air and liquid within the rectangular cavity of the tank. The four sides of the tank each have width W and height D (Figure 1). The height of the liquid in the tank is d. You can ignore any fringing effects and assume that the relative permeability of the material of which the tank is made can be ignored. Figure < 1 of 1 Air WO Liquid ∙W D K Electronic circuitry
Part A Derive an expression for d as a function of L, the inductance corresponding to a certain fluid height, Lo, Lf, and D Express your answer in terms of the variables L, Lo, Lt, and D. L-Lo d= 1,1 D L-Lo Submit Previous Answers ✓ Correct Part B What is the inductance (to five significant figures) for a tank full, full, full, and completely full if the tank contains liquid oxygen? Take Lo = 0.66000 H. The magnetic susceptibility of liquid oxygen is Xm= 1.52 x 10-3. Express your answer in henries to five significant figures. Enter your answers numerically separated by commas. 195] ΑΣΦ Se ? L1/4, L1/2, L3/4, Lfull = 0.66024,0.66048,0.66072,0.66096 H Submit Previous Answers Request Answer X Incorrect; Try Again; 2 attempts remaining Term 2: Review your calculations and make sure you round to 5 significant figures in the last step. Term 3: Review your calculations and make sure you round to 5 significant figures in the last step. Term 4: Review your calculations and make sure you round to 5 significant figures in the last step.
Part C Repeat part B for mercury. The magnetic susceptibility of mercury is Xm-2.9 x 10-5. Express your answer in henries to five significant figures. Enter your answers numerically separated by commas. L1/4, L1/2, L3/4, Lfull = Submit Request Answer Part D [5] ΑΣΦ For which material is this volume gauge more practical? Mercury O Liquid oxygen Submit Request Answer www. ? H 27