I'm searching for a circuit that turn on a led when the load is connected on its output, let's say for example a 5v power supply. I've seen few circuits that used two resistor in series with the positive supply rail, in order to make a voltage divider and drive a npn transistor, but in this way there will be a noticeable voltage drop on the load. Are there other way of detect a load?
Use a high side current sense amplifier (usually best with an instrumentation amplifier) followed by a comparator and switch.
Here is the basic idea:
By using a current sense amplifier, the resistor sensing the current can be small (less than an ohm).
Set Vtrip such that when the load current exceeds some threshold, the comparator turns on the transistor.
If you want to avoid a resistance in the load circuit, you could use a Hall sensor like this one. Such sensors measure the magnetic field generated by the current in the wire going to the load, and usually output you a voltage proportional to that current.