Let's imagine i just landed, and taxiing now to the gate. when i arrived there, i turned the fuel control.....

Question

.... switches to off (normal). but why is the cockpit light then turned of automatically, too? i mean, i did not have ground power, and the APU was not turned on at this point.

Answer 1

You probably have the emergency lights armed and they come on when you lose AC buss power. You have no AC power because you shut down then engines with no APU or ground power, so nothing is providing electricity except the main battery.

Answer 2

The AC generators trip off if they are going too slow (like when the engines stop turning).  The only things that are left are the essential DC bus and hot DC bus run off the battery and the essential AC bus run off an inverter powered by the battery.

All other AC systems would be inop as well as major DC systems that run off transformer/rectifiers powered by the main AC buses.

This is why you start the APU before shutting the engines off.  Some airplanes require the APU to be running prior to starting the approach for systems redundancy.

Answer 3

You had no source of electical power other than the batteries in the aircraft if the APU was not running, nor was their a GPU, so the aircraft's batteries were only powering the essential bus with the essential electial powered equipment. Im assuming that the cockpit light is not wired into the essential bus.