I'm curious to know how stand-alone tablets work, in particular how tablet pens work. How do they tell when they're being tapped without any batteries?
The pens often don't do much, in some cases they are just plastic. It is the tablett which does the work there are various ways that they can tell where they are being tapped.
Quoting from wikipedia
Passive tablets, most notably those by Wacom, make use of electromagnetic induction technology, where the horizontal and vertical wires of the tablet operate as both transmitting and receiving coils (as opposed to the wires of the RAND Tablet which only transmit). The tablet generates an electromagnetic signal, which is received by the LC circuit in the stylus. The wires in the tablet then change to a receiving mode and read the signal generated by the stylus. Modern arrangements also provide pressure sensitivity and one or more switches (similar to the buttons on a mouse), with the electronics for this information present in the stylus itself, not the tablet. On older tablets, changing the pressure on the stylus nib or pressing a switch changed the properties of the LC circuit, affecting the signal generated by the pen, which modern ones often encode into the signal as a digital data stream. By using electromagnetic signals, the tablet is able to sense the stylus position without the stylus having to even touch the surface, and powering the pen with this signal means that devices used with the tablet never need batteries. Wacom's patents don't permit their competitors to employ such techniques.
Active tablets differ in that the stylus used contains self-powered electronics that generate and transmit a signal to the tablet. These styli rely on an internal battery rather than the tablet for their power, resulting in a bulkier stylus. Eliminating the need to power the pen means that such tablets may listen for pen signals constantly, as they do not have to alternate between transmit and receive modes, which can result in less jitter.
Optical tablets operate by a very small digital camera in the stylus, and then doing pattern matching on the image of the paper. The most successful example is the technology developed by Anoto.
Early models were described as spark tablets -- a small sound generator was mounted in the stylus, and the acoustic signal picked up by two microphones placed near the writing surface. Some modern designs are able to read positions in three dimensions.
Wacom's are one example of a graphics tablet that works by generating and detecting an electromagnetic signal: in the Wacom design, the signal is generated by the pen, and detected by a grid of wires in the tablet. Other designs such as those by Pencept generate a signal in the grid of wires in the tablet, and detect it in the pen.
have also been designed to use an electrostatic or capacitative signal. Scriptel's designs are one example of a high-performance tablet detecting an electrostatic signal. Unlike the type of capacitative design used for touchscreens, the Scriptel design is able to detect the position of the pen while it is in proximity to, or hovering above, the tablet.
Most tablet pcs use Wacom pens and screen overlays. Which use an electromagnetic induction method to power and detect the position of the pen. Wacom tablets have a very high dpi (>1000) compared to the screens on touch phones or pda's which use conventional touch screen technology and have a substatially lower dpi.
The pen doesn't usually require power. The screen is what detects if pressure is applied.
For more information, visit How do touch-screen monitors know where you're touching?.
You could also use your finger instead of the pen; Neither one of them needing to the "powered" by batteries.