Electronic – How long does it take to recharge a car battery after starting

battery-charging

Assuming a typical lead-acid, 12 V car battery (typically at 13 V or so fully charged), and that it takes roughly 500 A over 3 seconds to start an engine, how long will it take to recharge the battery at any given charge rate?

Here's my attempt from what I remember about physics:

12.8 V * 500 A = 6400 W

Over 3 seconds that's 19,200 joules.

So, in a perfect world where all the current goes right back in to the battery and whatnot, how long does it take to regain all my joules and put them back in my battery?

Given a 2A charge rate:

14 V (output of charger?) * 2 A = 28 watts

Here's where I'm a little shaky. What's next? Divide the joules by the wattage to get time? Seems like it:

19,200 joules / 28 watts = 11.4 minutes.

That's it? 11.4 minutes at 2 A and all 19,200 joules are back? Seems hard to believe. My charger also has a 10A setting. So that means in about 2.5 minutes, it'll be "recharged".

So, are my assumptions correct? Do you really just use the charging voltage to calculate this, it seems like you would need to put the charging voltage in relation to the battery's capacity/voltage/whatever.

Best Answer

No, it isn't Joules in = Joules out. To a first approximation, it's Coulombs in = Coulombs out. It's the electrons flowing through the circuit that participate in the chemical reaction inside the battery (but not at 100% efficiency).

Forget about the energy/power/voltage calculation and just make the ampere-seconds for charging equal to the ampere-seconds for discharging, and then multiply by a fudge factor to account for the inefficiencies.

500A × 3s =1500 A-s = 2A × 750s = 10A × 150s

750s = 12.5 minutes

Figure about 90% efficiency, so the 12.5 minutes / 0.90 = about 14 minutes.