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Battery Pack Riddle
John and Alice are having a competition as to who can power their iPhone for the longest time. Both John and Alice have identical iPhones, a 70 cell (18650) battery pack, and DROK buck converters.

John's 70 cell battery pack is:  7S-10P, 24V... stepped down to 5-volt 1-amp

Alice's 70 cell battery pack is:  1S-70P, 3.7V... stepped up to 5-volt 1-amp

Whose battery pack will power their iPhone for the longest time, John's or Alice's?
That is am interesting question.
Thinking through it...
If the cells hold the same amount of energy, then the question is about getting that energy into the phone.
The higher voltage is good for getting the power through resistance in cables, but if the cable runs are short and the low voltage pack had low resistance cables, I think the main difference might be to do with the efficiency of stepping the voltage up or down to 5v.
Are the converters more efficient when stepping from 24v down to 5v, or when stepping from 3.7v up to 5v?
Electrically they have the same potential. If the cells are 2000mAh, then
10 * 2Ah * 25.9 = 518Wh
70 * 2Ah * 3.7 = 518Wh

As Oz brings out, the quest is the converters. The buck converter will actually be more efficient than the boost converter. Bucks basically pulse the input to keep a capacitor filled to a certain point as it's being drained (simplified version). Kinda like using a hose to keep a bucket full that has a hole in the bottom. This is of course if you get a PWM buck and not a linear regulator. Linear regs will actually be less efficient than the boost. These are the single chip voltage regulators common on the arduino's and other mcu's. They can only handle low amp loads, so not suitable for charging a device.

A boost converter on the other hand, has to use some fancy magnetic wizardry using a coil to push the voltage up. So this would be kinda like tossing cups of water up to fill the bucket. There are losses in the coil (an inductor actually) as the magnetic field charges/discharges. Plus the addition heat generated from the
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Buck converters only step down the voltage, so unless Alice as a [buck+]boost converter, she's out of luck.
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This all comes down the conversion efficiency.
Conversion efficiency is the key and that info is missing and therefore cannot be calculated.

And as Said Buck only goes down.
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