Simple Electrical Math

[Optimistic Paranoid]

Simple Electrical Math
 
POWER is measured in WATTS.  It’s named after the Scottish inventor James Watt, and it originally was used for measuring the power of steam engines.
For Electrical Power, 1 watt is defined as the amount of work done by 1 ampere of current, driven by 1 volt of electrical pressure.
Or as we’d write it as a simple math expression, 1W = 1A x 1V.

(I will mention in passing, that there is no difference between AC and DC, as long as we are talking about simple electrical stuff like electric heaters and motors and light bulbs.  When dealing with electronics, something else called REACTANCE comes into play with AC electricity, and there they talk about Volt-Amps instead of Watts.  You might see volt-amps mentioned on computer power supply bricks, for example.  The difference between watts and volt-amps is something only electronics engineers need to worry about, and we can ignore it.)

Now, obviously, if W = A x V, then 12 volts x 1 amp = 12 watts.  And 6 volts x 2 amps also = 12 watts.  This explains why the battery cables on the old 6 volt cars were much thicker than the battery cables on 12 volt cars.  They need to carry twice the current to produce the same power.

This also explains why the wires carrying DC power going into an inverter have to be MUCH thicker than the AC wires coming out of it.  If you want 1,000 watts of power out of the inverter, you need to take 1,000 watts of power out of the battery.  The inverter merely changes the power from DC to AC, and from 12 volts to 120 volts.  (We’re ignoring real-world internal losses in the inverter due to resistance and other factors like that pesky reactance.)

Let’s run the numbers.  Back in 9th grade math class, we learned that we could manipulate a simple formula like W = A x V to make it easy to find the unknown quantity if we knew any two values.  If W = A x V, then A = W / V, or V = W / A.

So 1,000 watts / 12 volts = 83.33 amps.  Whereas 1,000 watts / 120 volts = 8.33 amps.  This tells us that the inverter is going to draw 83 amps of current out of the battery at 12 volts, in order to send 8.3 amps of current out at 120 volts.

Notice that there is a 10 to 1 relationship between 120 and 12?  That gives us a simple, handy rule of thumb.  If the power supply on a computer or television or anything else lists how many amps of 120 volt AC it is going to use, we know that it will take 10 times as much DC current from the battery to run it with an inverter.  We don't even have to reach for our calculator.

Now, both Amps and Watts are instantaneous values.  That inverter is drawing 83.33 Amps of current RIGHT NOW.  It’s drawing 1,000 Watts of power RIGHT NOW.  Turn the inverter off, and current and power immediately stop flowing.  Neither Amps nor Watts is a QUANTITY in the same way that Gallons is.  Take 1 gallon of gasoline out of a fuel tank, and we all understand what that means.  A little economy car puttering around town may use half a gallon per hour, and a Nascar racer screaming around Daytona at 200 mph may be burning 5 gallons per hour.  So gallons is a quantity, and gallons per hour (gph) is a RATE.

Likewise, Amps and Watts can be thought of as Rates.  We are removing power from our battery at a RATE of 1,000 Watts or 83.33 Amps. For Quantity, we need to be talking about Amp-Hours or Watt-Hours.

 As discussed in another post in this series, the Quantity of electricity “stored” in a battery is measured in Amp-Hours.  If we left that inverter running for an hour, drawing 83.33 Amps, we would use 83.33 Amp-Hours.  Or, since it’s drawing 1,000 Watts, 1,000 Watt-Hours.

But since battery capacity is almost always specified in Amp-Hours, we’ll mostly stick to using that here.  (But note that 1,000 Watt-Hours is also called a Kilo-Watt-Hour – from kilo being the metric term for 1,000 – and your utility charges you by the KWH for the AC electricity you buy from them.)

We rarely run something like a microwave oven for a whole hour.  Here’s a trick for calculating Amp-Hours when you are measuring time in minutes instead of hours.

Because 1 hour contains 60 minutes, if we divide 1 by 60, we get 0.016.  In other words, each minute is .016th of an hour.  If we put a cup of coffee in our microwave to reheat, and it draws 83.33 Amps of current, that’s 83.33 x .016 = 1.33.  In other words, even though the inverter was pulling 83.33 Amps of current out of the house battery to power a 1,000 Watt microwave, we only pulled 1.33 Amp-Hours out of our battery bank to re-heat that coffee.

I hope that sheds some light on Volts, Amps, Watts, and Amp-Hours; and how they relate to each other.  Once you understand them, it’s easy to use a calculator to juggle the numbers around to make sense or it all.

Of course, the real world is never as neat as the mathematical one.  There’s inverter efficiency and something called “Peukert’s Law”, which we’ll get to another time, which prevents us from actually getting these mathematical ideals.  But it’s usually close enough for government work, as they say. Especially if we are talking about small numbers, like lights or a fan would draw, instead of large numbers like an inverter would draw.