(2) A variable dielectric capacitive displacement sensor consists of two square metal plates of side l =5 cm, separated by a gap of d = 1 mm. A sheet of

dielectric material 1 mm thick and of the same area as the plates can be slid between them as shown in below. Given that the dielectric constant (ɛ)of air is 1 and that of the dielectric material is 4: (a) Calculate the capacitance, C, of the sensor when the input displacement x = 0.0, 2.5 and 5.0 cm. (b) The sensor is placed into a bridge as shown below. Given V; = cos(400 n t) V , R3/R2 = 1, and the bridge is balanced when C = C min, find the output voltage, Eth , when the input displacement x = 2.5 and 5.0 cm.