Electronic – arduino – How to energize a 12v relay coil using a 2N2222 bipolar transistor

The first choice to make is whether you want to switch the input to the 12 V power supply, or switch the 12 V to the pump. If the pump spends a lot of time off, then powering down everything is probably a good idea. The 12 V supply will take some idle current, which is a waste if the 12 V isn't used for long periods of time. On the other hand, if the pump is on a lot and is turned on and off a lot, it will be easier to switch the 12 V to the pump. You could then even run the microcontroller off of the 12V, perhaps even with a linear regulator if you can keep its current down.

To switch the line power into the power supply, a plain old relay would be the simplest choice. There are plenty of relays that can be controlled from 5V that are intended to switch line power. Your supply will take well under 1 A, so there will be a wide choice of relays.

To switch the 12 V power to the pump, I'd probably use a transistor as a low side switch. Since the 12 V is already isolated from the line, you can tie the - side of the 12 V supply to the processor ground and use a direct connection. Lots of stuff can switch 1 A at 12 V. Here is a simple circuit:

You'll need a lesser-used (albeit still extant) monostable for this job instead of the 555. Given the voltage levels you are dealing with, 74xx parts are out of the question, which leaves us with the CD4000 family's monostables, in particular the CD4047 multifunction CMOS timer:

^{simulate this circuit – Schematic created using CircuitLab}

Notes and caveats: C1 must be a film type capacitor -- ceramics of that value aren't stable in value enough with voltage for timing applications, and the CD4047 requires a non-polarized cap to work. D1 can be swapped for a 12V zener if the relay turnoff is too slow for you. Q1 can be whatever small-ish power NMOS you have in your junk box (a jellybean BJT can be used provided you put an oh 1kOhm resistor on the base, too). The timing of the circuit is currently set for roughly 250ms, and can be changed by adjusting R1 and C1 in accordance with $$T_m = 2.48R_1C_1$$