# Current at 12 and 230 volts

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?

• Aside from the answer given bij Hearth, in practice a 100 Ah battery will last far less than an hour at 83 A. Nov 14, 2023 at 19:52
• An inverter is not a free energy source. Energy out < energy in. Nov 14, 2023 at 19:58
• simpler mentally to compare watts so you don't have to consider amps or volts ratios. Nov 14, 2023 at 20:27
• 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. Nov 15, 2023 at 4:24
• 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) Nov 15, 2023 at 8:58

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

The heater draws 83.33 A from the battery.

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

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.

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.

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.

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.