If your tank is hot, use a test lamp (NOT A NEON SCREWDRIVER) between neutral and the output of the thermostat.
Turn the temperature up and down and the light should turn on and off
(you should hear a very satisfying click as you do this.)
If the tank is cold (because the stat maybe doesnt work)
Remover the stat from the tank and connect a continuity tester between the terminals. Set the stat for a low tempeature (30ºC ish).
You should get continuity.
Boil a kettle full of water and pour it over the stat's rod.
You should lose continuity.
To test the element, you need to do two tests - a continuity test between the two terminals will show that the element is not broken.
You should also do an insulation test between the immersion's terminals and earth - this will check that water hasn't got into the element.
(You'll need a proper insulation tester for this one.)
When the thermostat gets hot (over its set temperature) it turns off.
I have told you how to test this works.
Did you want to calibrate it so you can be sure it turns off and on at exactly a particular temperature?
That is much more complicated.
When you stuff 230 volts up the element it gets hot.
I have told you how I would test it to ensure that it is OK to put voltage on it.
That's it. Thats how I do it. I'll bet there are other approaches like switch it on and see if the water gets hot,
Then turn down the stat and see if the water gets cold....
But that takes hours and I don't have hours.
Would it be easier if you were to say if you actually have a problem with an immersion heater?
A simple basic way to see if it is running is watch the electric meter as someone operates the water heater spur/ switch, generally domestic ones are 3kw and you see the meter speed up.
If you have a clamp meter and KNOW how to SAFELY use it, the meter tails will show an increase of approx 13 amps.
TTC' s way is the proper and AFAIK the only way to test it before powering it up, if the element is suspect.
A live to earth fault is quite common once the element erodes and splits.
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