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I have three mobile phone chargers with rating 5V 500mAh, 5V 1Ah , 5V 2Ah. When I charge my phone Mi 4i with these chargers , the charging time is different. It means all these chargers drive different current through my phone's charging circuit.

So my question is, how can same voltage sources(5V) drive different current ( here 500mA , 1A and 2A) through same load(my phone)??

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    \$\begingroup\$ It means all these chargers drive different current through my phone's charging circuit. NO they don't and the will not How much current flows is determined by the phone not by the charger. The name "charger"is actually wrong, they are "power adapters". The actual charging circuit is close to the battery Inside the phone. Some power adapters can deliver more current and then some phones also take more current to charge the battery faster. \$\endgroup\$ May 14 '16 at 20:52
  • \$\begingroup\$ So my question is, how can same voltage sources(5V) drive different current ( here 500mA , 1A and 2A) through same load(my phone) I hope you now understand that this does not happen, the phone determines the current, not the charger / power adapter. \$\endgroup\$ May 14 '16 at 20:54
  • \$\begingroup\$ Phones have 'local intelligence' to manage battery charging (it is the real charger), it isn't defined by the 'charger' which just supplies current at a voltage. So a trivial answer is the phone charger only consumes as much as the 'charger' can supply. By default USB only supplies 500mA. So a smarter answer is a 'real' phone 'charger' (thing plugged into the wall) is detected by the phone charger circuit, the ability to supply more current is understood by the phone's internal charger, and it works out how much current it can consume; with a dumb USB 5V adapter it only takes 500mA. \$\endgroup\$
    – gbulmer
    May 14 '16 at 20:57
  • \$\begingroup\$ Put another way, it isn't the 'same load'. The phone's internal charger adapts to the power supply, and presents a different load to the different chargers. \$\endgroup\$
    – gbulmer
    May 14 '16 at 21:01
  • \$\begingroup\$ @FakeMoustache if I connect a 12V 7.2Ah Lead Acid battery through dc voltage regulator(5V) instead of adapter to charge my phone , will my phone draw higher current (say 4-5A ) to charge it faster and will it damage my phone?? \$\endgroup\$ May 14 '16 at 21:03
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The current control is implemented by the power management logic implemented in the phone. In particular, according to the Mi 4i FAQ, your phone uses Qualcomm's original QuickCharge 1.0, which consists primarily of two components: AICL = Adaptive / Automatic Current Control, and APSD = Automatic Power Source Detection.

APSD incorporates BC1.2 = Battery Charging Revision 1.2, an extension of the USB standard that allows chargers to communicate that they can deliver higher current, e.g. by shorting the D+ and D- lines.

AICL includes heuristics for automatically detecting the current limit of the power supply by slowly stepping up the input current (e.g. in 25mA steps). Usually this is limited to about 2A.

You ask in the comments if you can safely charge your phone using a DIY charger using a 5V regulator. Generally this should work fine as long as you include the appropriate BC1.2 signalling to the phone. To do that you can either construct your own fast-charge cable with the D+ and D- wired as needed (see below), or you can buy various fast-charge USB adapters, e.g. search on "CW3002" on eBay to locate adapters using a common CellWise CW3002 controller.

Below is a bit more info on the technical details, first on on AICL, from the NXP (freescale) BC3770 datasheet, and second on BC1.2 from Maxim's Overview of USB Battery Charging Revision 1.2 and the Important Role of Adapter Emulators. Now that you know the appropriate buzzwords you should be able to dig deeper if need be.

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There are 2 types of charging IC's used in cell phones. The 'dumb' IC uses a standard 1 amp charging current if the wall adapter can supply it. If you use your PC to charge the phone, it may only allow 1/2 amp of charging current, so that is all the charger IC has to work with. It will not use so much current that the source voltage drops below 4.0 volts. This includes a drop of 1/2 volt in the cable going to the wall-pack.

The 'smart' IC in some smart phones will draw as much as 2 amps to charge the phone, if the charger can supply 2 amps and still maintain close to 4.5 to 5 volts under that load. It is generically called a 'fast' charge, and is usually controlled by a check box in the phones 'Battery' control directory. A phone that charges at 2 amps will come supplied with a 2 amp charger (wall-pack).

My Samsung Note 2 has such a charger and I have it set for 'fast' charge. The charger IC in the phone makes all the decisions about how much current there is to charge with, is there a 'fast' charge setting for this phone, is the supply voltage at least 4.5 volts, plus monitoring the charging of the battery and reporting charge status to the CPU. It is a very busy IC when charging.

NOTES:

1) The LM7805CT has a limit of 1 amp with heatsink, but there are simple booster circuits you can find on the web. A 12 volt 7.2 amp-hour battery will work, within the constraints of the LM7805CT IC.
2) My answers in terms of current are in amp-hours or mA-hours.
3) I am not implying a charge current > 2 amps or a charge voltage (at the phone) > 5.1vdc. I have not yet seen any phones capable of going out of these ranges.

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I think there is a fundamental misunderstanding here. Are your 3 "chargers" connected to a wall are they just yanother battery? If your charger is rated at 500mAh or 1Ah these are ratings of CHARGE, not of CURRENT.

Backup batteries are rated in terms of charge. Many of these are on the market. You charge the backup battery first and then use it later when your phone battery is low.

An AC adapter that changes 120 VAC into 5V DC would be rated in Amperes and not amp hours or milliamp hours.

1 Ampere = 1 Coulomb / Second which is a flow rate of charge

1 Ah = 1 C/s * 3600 s = 3600 C of charge

Obviously if the phone can draw more current, it will charge the battery faster. This article explains it much better than I can.

So in order to answer your first question, what were the charges on each of the backup batteries? What is the maximum charge of your phone battery? If the backup battery cannot provide enough charge, your phone battery will not be fully charged.

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