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Off delay timer needed

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Here's the setup: I have a Velleman Liquid Level Controller K2639. It has a relay rated for 120VAC at 3A (although I don't think the track spacing on the PCB meets UL requirements, but that's another story). I am going connect the relay to an SSR (a Crydom EZ240D18) to control the pump to empty the tank. This also avoids having 120VAC on the PCB. What I need to do is delay the off time for the relay such that when the controller detects the low level and opens the relay the pump stays on. I am aiming for 2-3 minutes longer.

The datasheet for the SSR indicates 15mA draw at nominal voltage of 24VDC. I will be at 12VDC or maybe 5VDC, as you will see why below. I am thinking I could parallel a large capacitor across the SSR terminals. The fact that this will cause a delay when the relay closes and the capacitor charges is a non-issue. Capacitor discharge rate is t=RC, R of the SSR is approximately 1600 ohms (24VDC/15mA) and with t=160sec (round number), C=0.1F. So far so good?

I found .22F, .33F, and 1F at All Electronics, all of which are 5.5V. How fast can and should these large caps be charged?

Here's my thought. Use a 7805 to regulate down the 12VDC from the PCB to charge the cap and drive the SSR. Place the cap and SSR in parallel and a current limiting resistor between the 7805 and the cap/SSR combo. The relay contacts will either be before or after the regulator or current limiting resistor, doesn't really matter. This leads back to my previous question, how much current should I allow to charge the cap?
 
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There's no particular limit on how fast you can charge the caps. They are not like batteries. They'll take anything the 7805 can deliver. Just select a resistor to limit the current to the maximum current you can draw from the 12V supply.
 
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