Is there a way that I can make an Arduino or other Micro-controller detect a change in capacitance?

I'm thinking of having a screen on my door that only turns on when you touch the metal door handle.

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Yes.

Simplest way would be to use a high value resistor (1-10M) and follow the instructions on this old arduino forum post: http://www.arduino.cc/cgi-bin/yabb2/YaBB.pl?num=1171076259

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One of the best ways that I've found to measure capacitance is to use an RC circuit. Use a digital I/O port on a microprocessor to charge and discharge the capacitive sensor through a fixed resistor. Start a timer when you begin the charge/discharge cycle. Then use a comparator to detect when the capacitor has fully charged/discharged. Stop the timer when the comparator trips. The value stored in the timer can then be used to calculate the capacitance of the sensor.

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Not an Arduino specific answer, but Microchip have an explanation of one way to do it on the PIC - which would possibly work on an AVR

http://www.microchip.com/stellent/idcplg?IdcService=SS_GET_PAGE&nodeId=1824&appnote=en545264

Only concern with these methods is lack of protection from static discharge

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Why don't you go for multitouch capacitative sensibilities (having read tutorials from various capacitative touch semiconductor makers whose stuff's available from stock at Arrow or DigiKey or Mouser) and see how close you can get? If you aim low and miss, you don't learn as much....

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