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Suppose that I have a lead acid battery that:

  • Can (and will) be discharged by using 70% of its energy (energy left is 30%)
  • When the battery is at 30%, I will recharge it at 0.8C.

How long will the battery need to be completely charged?

My reasoning would be the following: $$V_n = 100 V$$ $$Capacity = 50Ah$$

Then the (theoretical) energy that the battery can deliver is 100*50=5 kWh. If I use 70% of it then that 70% is 3.5 kWh. To get the battery back to its original state (neglecting charging efficiency) I need to put 3.5 kWh back into the battery. If I recharge it at 0.8C=40Ah assuming 40 A of current through the battery then $$t=3.5kWh/(100 V *40 A)=3150 s = 52.5 minutes$$

Bonus point: What does recharging a battery at 0.8C means? 0.8C is a measure of capacity but in practice I'll have a current running through the battery terminals. How do I reconcile the two?

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  • \$\begingroup\$ Note that you don't want to charge lead-acid cells at constant current. The typical lead-acid (and LiPo) charging profile is CC/CV, meaning you start at a constant current that's chosen for the capabilities of the charger and the battery, then when you hit a threshold voltage (4.2V/cell for most LiPos, 2.god-I-don't-remember for lead-acid (2.2 to 2.4, and it varies with temperature)) you hold it at that voltage and let the current be whatever it needs to be. \$\endgroup\$
    – TimWescott
    Commented Sep 10, 2019 at 21:46

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1C charge or discharge rate is one battery capacity per hour. As the capacity is given in Ah, Ah/h = A.

If you've discharged 70% of your capacity, and recharge at 0.8 (80%) of your capacity per hour, recharge will take about an hour.

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