About electricity. The reason for the issur of electricity is the matter of much debate. The one that i am most familiar with, is the issue of the spark. I posted something earlier about there not being a spark in devices like cell phones or laptops. I have done some further research into this, and it appears that my first source was mistaken.
Even so, there may be other issues. I don’t really know much about the inner workings of a cell phone. I don’t know when and how the spark is created. In a regular light switch, it happens the instant you flip the switch and complete the circuit. It is possible, from my perspective of relative unfamiliarity with the workings of a phone, that the spark is a grama.
I don’t know if that makes it mutar, but it certainly makes it much less of a chilul shabbos.
I think that the other main shita, besides for those that hold that electricity is derabonon, is that since a light or a fan is attached to the house, by completing the circuit you are doing boneh.
This definitely would not apply to a cell phone, which is not connected to the house (even a connection with a charger i don’t think is a connection for this, because when you turn on the phone you are completing a circuit that is wholly within the phone, and is still not connected to the house. That would be for using the phone while it is plugged into the charger. As for plugging the phone into a charger that is connected to the wall, i don’t know how that circuit works.)
Again, i have never really studied the issue/sugya of electricity on shabbos at length, in a concentrated manner. Those who did would probably be able to find various issues with this comment, whether leheter, or li’issur. But “Kach hie darkah shel torah…”