(3) A capacitance level transducer is to be used to measure the depth h of liquid in a tank between 0 and 7 m. The total length l of the

transducer is 8 m and the ratio b/a of the diameters of the concentric cylinders is 2.0.The dielectric constant ɛ of the liquid is 2.4 and the permittivity of free space ɛ, is 8.85 pF/m. The transducer is incorporated into the deflection bridge as shown in figure with R2 = 100 Q, R3 = 10 kQ and Vs = 15cos(400 nt)V. (a) Calculate the value of Co so that the amplitude ETh is zero when the tank is empty. (b) Using this value of Co, calculate ETh at maximum level. (c) Explain why the relationship between ETh and h is non-linear and calculate the nonlinearity at h = 3.5 m as a percentage of full-scale.