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I had a quartz wall clock in my workshop that ran a AA battery power. The battery died so I decided that rather than buy a battery, it would be more fun to convert the clock from battery power to AC power.
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For this project, the only tools that you'll need are a soldering iron and (optionally) a hot glue gun.
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Here in the pacific Northwest, I pay about $.08 per kWh for residential electricity. This clock power supply circuit uses about 17.5 mW. So here is a rough calculation of the cost to run this clock for one year ..
$.08/kWh x (.0175Wh x 24 x 365) / 1000 = $.012 per year
Regards,
Scott
Since that's a joker which has to be measured we can't fint out if it's actually cheaper.
Also I don't know what a discount alkaline battery costs in your country but here it's available for what is less than USD ½.
But really it's not the cost that concerns me most. It's the power out issue as a normal quartz clock will resume from where ever it was and cause you to not immediately notice the time shown is incorrect.
Also a standard quartz clock is not very precise so to stay within acceptable offset from real time you have to adjust it at approx. once a year anyway (if you're lucky it's too fast so just cut the power for a few moments). An ordinary consumer quartz movement today is specified to be within 0.5 - 2 seconds pr. day. Typically somewhere between 0.5 and 1 second can be expected of the ordinary consumer movement except for very few lucky samples (majority are specified within 1 sec but can also be specified for 0.5 for the best or 2 sec for discount movements). Even 0.5 sec/day which to many people doesn't seem as much accumulates to 3 minutes/year.
The power out issue you can deal with however. It can really be almost as simple as a triac and a push button. So if power fails the clock won't restart automatically upon return of power and you'll notice immediately it's wrong. Push the button to start the clock (and of course set it again).
Or why not just make something with a few super capacitors and a solar cell to skip mains power altogether if you really want it to be battery less?
I bet it easily chews more on your electricity bill than one cheap battery costs every year.
Also since it's not radio controlled you can easily be confused whether it shows the correct time if there has been a power out while you've not noticed it since the clock will run again afterwards. With a battery it'll stop when it's out of power so you will instantly notice if it's wrong.
You can instead use an RC movement with all those benefits they have but then you need to use a good power supply without high frequency noise (the easiest and most durable is an old fashioned one with iron core transformer).
Also you can add a backup with a super cap in parallel with the movement but I bet you need more than just a small one to get any significant run time.
If you want long run time before having to chance the battery I'll recommend putting in several single AA battery holders and wire them in parallel to feed the clock. And (very importantly!) install those energizer AA "L92 1,5 volt" lithium batteries in them. Important because ordinary batteries will leak before they're even half empty if used in such long time application. Also important to only parallel connect batteries of equal charge state. So when finally replacing them take them all out before putting the new ones in. Voilá. With a small handful of them you'll have a clock that easily runs for 8-10 years and even 15 or more is possible.