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I hope someone can help explain this:

Say I have a 12 V 100 Ah battery and a heater that uses 1000 watts.

At 12 V we'll get 1000 / 12 = 83.3 amperes, so the battery will last a little over 1 hr.

If I use an inverter to convert the 12 V to 230 V we get:

1000 / 230 = 4.3 amperes. Now the same battery will power the heater for 23 hrs.

How can the same battery have two different power levels? I must be doing something wrong.

Can someone explain my mistake please?

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    \$\begingroup\$ Aside from the answer given bij Hearth, in practice a 100 Ah battery will last far less than an hour at 83 A. \$\endgroup\$
    – StarCat
    Nov 14, 2023 at 19:52
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    \$\begingroup\$ An inverter is not a free energy source. Energy out < energy in. \$\endgroup\$
    – winny
    Nov 14, 2023 at 19:58
  • \$\begingroup\$ simpler mentally to compare watts so you don't have to consider amps or volts ratios. \$\endgroup\$
    – dandavis
    Nov 14, 2023 at 20:27
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    \$\begingroup\$ If the inverter is 100% efficient, the power out equals the power in. If it is putting 1kW out, then it needs 1kW in, which, at 12V will correspond to the 83.3A. \$\endgroup\$
    – copper.hat
    Nov 15, 2023 at 4:24
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    \$\begingroup\$ It's worth being clear that your heater is only going to put out 1000W at its rated voltage. A 230V 1000W heater connected to 12V won't even get hot enough to feel unless it's very compact (and any fan won't turn). Conversely a 12V heater run at 230V will get very hot, and possibly very bright, but only for an instant (unless it catches fire) \$\endgroup\$
    – Chris H
    Nov 15, 2023 at 8:58

4 Answers 4

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Case 1: Using a 12 V - 1 kW heater.

enter image description here

The heater draws 83.33 A from the battery.

Case 2: Using a 230 V - 1 kW heater and an inverter.

enter image description here

The heater draws 4.35 A from the inverter which, in turn, draws 83.33 A from the battery (assuming 100 % inverter efficiency).

The error is in presuming that only 4.35 A is drawn from the battery.

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The inverter passes power (voltage times current), not current, so a perfect inverter would still draw 83.3 amps from the battery.

Real inverters are not 100% efficient, so your inverter may draw close to 100 amps, and the battery voltage will drop somewhat when delivering that current, so the inverter will draw still more current.

The Ampere-hour rating of a lead-acid battery is based on a 20 hour discharge rate (5 A for a 100 Ah battery). If you draw a higher current, you will get fewer than advertised Ah. A table I have says that if you discharge a 100 Ah battery at 25 A, you will only get 72 Ah from it.

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The current through the load isn't what matters here; it's the current through the battery that matters. Assuming an ideal converter, the current through the battery in both cases will be identical and equal to 83.3 A.

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The easiest way to approach this kind of issues I found is to always reduce to power instead of using current/voltage.

In this case the battery has 12V x 100Ah = 1200Wh of power, meaning that the heater can be turned on for 1200Wh/1000W = 1.2h. Assuming everything ideal (ideal battery, ideal inverter etc...) this isn't going to change if you have an inverter in the middle.

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