A capacitive displacement transducer is designed to determine the rotary position from 0°→180° as shown in Figure Q3. The moving plate whose radius is 40mm is sandwiched between two fixed plates, spacing at 1mm. The dielectric constant of air is k = 1.The capacitive transducer is formulated as: C = farads d where; dielectric constant A = the area of the plate, in square meters €o = 8.854 x 10-12 in farads per meter = the plate spacing in meters k %3| d (a) Produce an equation of the change of the capacitance (F) when the moving plate is rotated from 0°→180°. (Hint: The circle area.) (b) Calculate the capacitance if the rotational angle is at 90°.

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Please answer a and b.

A capacitive displacement transducer is designed to determine the rotary position
from 0°→180° as shown in Figure Q3. The moving plate whose radius is 40mm is
sandwiched between two fixed plates, spacing at 1mm. The dielectric constant of
air is k = 1.The capacitive transducer is formulated as:
C =
farads
d
where;
dielectric constant
A = the area of the plate, in square meters
€o = 8.854 x 10¬12 in farads per meter
d = the plate spacing in meters
k
(a)
Produce an equation of the change of the capacitance (F) when the moving
plate is rotated from 0°→180°. (Hint: The circle area.)
(b)
Calculate the capacitance if the rotational angle is at 90°.
Transcribed Image Text:A capacitive displacement transducer is designed to determine the rotary position from 0°→180° as shown in Figure Q3. The moving plate whose radius is 40mm is sandwiched between two fixed plates, spacing at 1mm. The dielectric constant of air is k = 1.The capacitive transducer is formulated as: C = farads d where; dielectric constant A = the area of the plate, in square meters €o = 8.854 x 10¬12 in farads per meter d = the plate spacing in meters k (a) Produce an equation of the change of the capacitance (F) when the moving plate is rotated from 0°→180°. (Hint: The circle area.) (b) Calculate the capacitance if the rotational angle is at 90°.
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