A variable dielectric capacitive displacement sensor consists of two square metal plates of side 5 cm, separated by a gap of 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 the figure. Given that the dielectric constant of air is 1 and that of the dielectric material 4mm, calculate the capacitance of the sensor when the input displacement x = 0.0, 2.5 and 5.0 cm.

X E1 Variable dielectric C = 2 E01A E02 A + d d Since A = wx, A = w(1-x), when w is the width of the plates, d = 1 mm w = 50 mm - 1 = 50 mm 8=854x10-12 (F/m) C= Eow d Equivalent to C1 // C2 CT=C1 + C2 [l ( )x]