How do you know if the current in the solenoid id turned on?

You can determine if the current in a solenoid is turned on by using a multimeter to measure the voltage across the solenoid or the current flowing through it. Additionally, if the solenoid is energized, you may feel a magnetic field around it, which can be tested with a small ferromagnetic object that will be attracted to the solenoid when current is present. Lastly, if the solenoid is part of a circuit with an indicator, such as a light or LED, it will illuminate when current flows.