[Departed]

Hi. The transponder doesn't rely on the battery. The coil around the ignition lock transmits a signal to the chip. The chip powers itself from this signal, and modulates the signal to talk to the immobiliser. The immobiliser also modulates the signal to talk to the chip. It's triggered as you turn the key from off, to accessory.

The battery is for the remote control: in the same box as the transponder, but not connected to it. The transponder has nothing to connect it to anything. You could take the battery out, and the transponder will still work. In fact early cars were meant to have one normal key an one key with only a transponder. Don't know whether this ever happened, but it would explain why so many early cars have only one key.

As I said earlier, the immobiliser would be a little pointless if it could be overcome without a good deal of effort: whoever wanted to steal your car would simply switch off the immobilser and drive your car away.