One common kind of computer keyboard is based on the idea of capacitance. Each k

Question

One common kind of computer keyboard is based on the idea of capacitance. Each key is mounted on one end of a plunger, the other end of the plunger being attached to a movable plate. The movable plate is separated from a fixed plate, the two plates forming a capacitor. When the key is pressed, the movable plate is pushed closer to the fixed plate and the capacitance increases. Electronic circuitry enables the computer to detect the change in capacitance, thereby recognizing which key has been pressed. The separation of the plates is normally 5x10-3m but decreases to 0.150x10-3m when the key is pressed. The plate area is 9.50x10-5 m2 and the capacitor is filled with a material whose dielectric constant is 3.50. Determine the change in capacitance that is detected by the computer.

Explanation / Answer

The formula you need to use is: C = ? e A / d C = capacitance ? = dielectric constant A = area of one of the plates e = 8.85 x 10^-12 farad/ meter d = distance Then just insert the values to find the Capacitance when d = 0.550 mm (or 0.0550 x 10^-3 m), but be careful because the A was given in mm. It has to be in m2, so A = 4.65 x 10^-5 m2 C = 2.80 x 10^-12 F Rearranging to make d the subject (to find d when capacitance is 0.473 x 10^-12 + 2.80 x 10^-12 = 3.273 x 10^-12 F): d = ? e A / C d = 4.71 x 10^-4 m or 0.471 mm The initial separation is 0.550 mm, so just subtract d from this answer. Answer = 0.550 - 0.471 = 0.079 mm

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