Frigidaire Stove - bottom element burnt out. Replaced the element but the breaker would "pop" every time I turned it on. Removed the new bottom element and discovered one wire came off during the installation. Suspect it grounded out and was the cause of the breaker tripping. No signs of burning or damage on the wire so I connected the wire again, checked tightness and reinstalled. The element is working find now. Problem - now the oven cooling fan does not turn off. Could I have damaged a control module or the sensor that turns the coolilng fan on and off?

If element caught on fire, I would suspect stove needs cleaning. Do that then elements should not smoke for long. (I hope all moisture was removed from stove!!!)

I THINK THE HEATING ELEMENT YOU GOT COULD BE WRONG SIZE. I KNOW MINE WENT OUT WHEN COOKING SOMETHING HOTTER THAN I USUALLY USE LIKE 450 DEGREES, IT BURNT OUT. BY CLEANING OUT YOU'RE OVEN, WHICH REQUIRES REAL HOT TEMPERATURES, IT SOUNDS LIKE YOU ON THE RIGHT TRACK. IT BEING OLDER STOVE, A LOWER RATED ELEMENT I WOULD TRY..

The pop was a shorted wire.
The short drew sudden over-amp at breaker.
Amps = heat.
Breaker senses heat and trips before wire to oven is damaged, and before the arcing short can cause a fire.
Was the short at the element?
I don't know, but sounds like the circuit board was damaged.
Of course they are putting electronics inside all appliances today instead of old mechanical dial, because it's cheaper or so much prettier... but new appliances more vulnerable to surge, and other electrical failures. Which is true for all 240V appliances not protected by whole house surge protector.
To test element.
Remove element.
Use a continuity tester across the element connections.
If there is continuity, then the element is probably functional.
Use a multimeter across same element, set multimeter to read ohms.
240 Volt, 3500 watt element should be about 16 ohms.
4500 watt about 12-13 ohms
Volts squared divided by watts = ohms
57,600 divided by 4500 watt = 12.8 ohms
http://waterheatertimer.org/images/ohm-reading-for-emements.jpg
http://waterheatertimer.org/See-inside-main-breaker-box.html

I would guess that the short fried the circuit board, but there is a also a shorted wire somewhere that is still bare and dangerous while power is ON and you are touching oven or stove, unless 240V breaker is GFCI or arc fault, which probably not. Especially dangerous if you are moving stuff around trying to find problem while power is ON.
Gene
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If you need further help, I’m available over the phone at https://www.6ya.com/expert/gene_9f0ef4df2f9897e7

look for a shorted bake element .. you should be able to see where it poped. ( some times ) if you have ohm meter you can ck for an open element . **** //

Sounds like the loose oven element caused a short circuit, which may have fried a wire inside the range. Or, it may have tripped the circuit breaker (or blown the fuse) for the range circuit. Check your electrical panel. If the circuit is open, don't reset it until you've removed the remnants of the oven element.

THE ELEMENT SOUNDS LIKE IT IS SHORTED BIG TIME TO TRIP 100 AMP BREAKER. I CAN'T SEE WHY A ELEMENT BEING TOUCHED WOULD DO THAT. CHECK THE WIREING TO THE ELEMENT AND MAKE SURE NOTHING ELSE HAS SHORTED TO ALSO CAUSE THIS PROBLEM, PLEASE TURN THE POWER OFF FIRST. BUT THE ELEMENT CAN BE REPLACED AND NOT THE WHOLE STOVE

The element burnt in to and arced which is the loud noice you heard red flash of light. It probably tripped the breaker at the electrical panel. Don't turn it back on until someone checks the element and replaces it.

the pop is most likely an electrical short it will be in the back of the stove,that is unless your new element shorted .when cool you can run your hand around it and you should feel no blisters,smooth only.other wise you are doing a visiual inspection and looking for an obivous burnt wire/connection.God bless ,tom

it sounds like a wire from the bottom element in the oven shorted.check the circuit breakers to see if there tripped,if so reset it and try the oven,let me know.