A parallel - plate capacitive transducer having air as dielectric between the plates, plate area is 50 mm × 50 mm and plate spacing is 0.5 mm. The displacement causes the capacitance to change by 10 pF. The sensitivity of the capacitive displacement transducer is:

 

A parallel - plate capacitive transducer having air as dielectric between the plates, plate area is 50 mm × 50 mm and plate spacing is 0.5 mm. The displacement causes the capacitance to change by 10 pF. The sensitivity of the capacitive displacement transducer is:

• A. 50.23 pF/mm
• B. 66.67 pF/mm
• C. 61.25 pF/mm
• D. 59.12 pF/mm

Answer: Option B

Solution: C =  ε * A/d

or, C =8.854 *10^-12* 50*50/0.5*10^-3 = 44.27 pF

sensitivity = Δc/Δd

or, sensitivity = -ε * A/(d^2)

or, sensitivity = - 8.854 *10^-12* 50*50/(0.5*10^-3)^2 = 88 pF (approx)