what size battery do i need to run a 1200 watt inverter

It seems like Tesla might be making a battery for your house. Would that exist cool? I recall so. But why would you demand a house bombardment? I can call up of a couple of uses:

• For an off-grid house you might like to power information technology with solar or wind ability. Unfortunately, neither of these two sources provide constant energy. If you lot could store the energy in a bombardment, yous could use this during the dark or calm weather condition.
• Many people go on a gasoline powered generator for their house. I have i that I don't employ too oft, but it's awesome when y'all need information technology. What if you had a bombardment that yous could use for your business firm in times of power outages? That would be absurd.
• It seems like the power company would like everyone to take a bombardment. With a firm battery, y'all could reduce power spikes on the grid. When you plow your air conditioner on, it draws a large electric current for a curt period of time(here's an caption of why the electric current spikes). With a bombardment this current demand could be leveled out (I guess).

But that's not why you are here, is it? You want to know how big of a bombardment y'all would demand. Permit'southward find out.

Battery Size

We need some starting values. First, how long exercise y'all want to run your firm on a bombardment? I think Elon Musk (from Tesla) said one week. Got it. The side by side big thing is the power usage. I call up a off-white assumption is a constant 2000 Watt power usage. Conspicuously a house would need more than 2000 watts at some signal in the day. Even so, at night y'all wouldn't demand much power such that the average for the day could be 2000 watts. If you don't similar that value, you can put your own numbers into the calculations.

If I know the power and the time, I can utilise the definition of power to calculate the energy stored in the battery.

Having the power in Watts is fine (since a watt is a Joule per second) but I demand the fourth dimension in seconds.

Now I can calculate the stored energy in the battery.

Not bad. But what the heck is a Joule? Sure, information technology's a unit of free energy merely is that a large amount? Here'due south a simple experiment you lot can exercise yourself. Take a textbook and put it on the floor. At present pick information technology up and put it on a table. In order to elevator the volume, you need energy (to modify its gravitational potential free energy). A book is near 1 kg and you lifted it nigh 1 meter. That makes a alter in energy of virtually x Joules (don't forget the gravitational field is 9.8 N/kg). So at present yous know about Joules.

Now for the battery size. The dimensions of the battery volition depend on the blazon of battery. The current Tesla vehicles use a lithium ion battery. According to Wikipedia, the lithium ion battery has an energy density from 0.9 - two.23 MJ/L (mega Joule per liter). I would imagine that Tesla would only use THE BEST BATTERIES! That would put its energy density at 2.3 x x⁹ Joules per cubic meter.

If I call the free energy density σ, then I tin observe the battery volume:

Putting in values for the energy density and the bombardment energy:

So just half a cubic meter. That's non too bad. If you want to put this inside your house, you could make information technology as tall as a wall (let's say 2.v meters). Now from a design view mayhap a battery should be simply 5 cm thick. This ways that it would accept to be about four meters wide. Ok - that wouldn't work. If increase the thickness to 10 cm, it would just be 2 meters wide. That could work.

Of form, this merely really works because of the high free energy density for a lithium ion battery. If you used an akaline battery (like AAs) it has a lower free energy density at around 1.8 MJ/50 such that it would be slightly larger firm bombardment (merely not rechargable). You tin can look at the Wikipedia page on energy density to go an guess for house batteries of different materials.

Just for fun, what if yous fabricated a penny battery (from copper-zinc pennies and acid)? How big of a bombardment would yous need in that case? Here is your answer.

Homework

This is just a perfect story for homework. It won't be as well difficult, and so don't delay and start soon.

• What if y'all wanted to run your business firm on AA Jail cell batteries? From my previous investigation, I found that a AA bombardment has about ten,000 Joules of stored energy. How many AA batteries would you lot need and how much space would information technology take up?
• What if you wanted to run your house on a nuclear ability plant that used Thorium? How much Thorium would y'all need? Use the energy density from Wikipedia.
• According to this news, Apple will build a 130 MegaWatt solar farm to use for its stores and stuff. What if you wanted to run your firm completely off grid with solar panels and batteries. How big would the solar panels be? You can assume the Sunday gives m watts per foursquare meter with a solar panel efficiency of about 25%. Don't forget that the Sun won't always exist directly perpendicular to the panels. This mail service might be useful.

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Source: https://www.wired.com/2015/02/size-battery-need-power-house/

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