# Basics of Electrical units and quantities

I’m sick and tired of stories in the general boating press by confused writers that mix up electrical numbers and quantities.

This is probably because electrical units are a bit different than the units used for length, speed and distance.

Here’s my feeble attempt at clarifying this apparently confusing matter. I shall compare electrical current to water current flowing in a circular pipe, which seems appropriate in our nautical environment.

**Some theory first**

Let’s start with the three most familiar units:

**Voltage**– The eagerness with which electrons want to flow from A to B. In our comparison, this is equivalent to the water pressure in a pipe.**Current**– The magnitude (amount) of electrical charge passing through the conductor per unit of time. In our comparison, this is equivalent to the discharge of a river or pipe. Discharge is usually measured in cubic meters per second, likewise electrical current is measured in coulombs per second. An electrical current of 1 ampere is defined as 1 coulomb per second. This is important to note: current is a derived quantity. One coulomb is just a large bunch of electrons, about 6.241 x 1018 of them.**Electrical energy**– The thing that we have electricity on a boat for anyway. Electrical power is what makes the appliance (winch, coffee maker, light bulb) work. In our comparison, it is the amount of power that a turbine could transfer from the water in the pipe. This is a product of the discharge and the pressure. Likewise, in an electrical circuit the power is the product of the voltage and the current. In units: volt times ampere equals watt (**V * A = W**). (Note to fellow engineers: I know it should be U * I = P, but let’s not further complicate matters. I am also not complicating things further by adding AC power phase.)

Note that although voltage and current are used so often, they are NOT basic units such as volume and length are. In particular voltage is defined as the total energy required to move an electric charge from A to B divided by the magnitude of the charge. Current is also a derived value. In electricity, the basic unit is **charge** measured in **coulombs**.

The confusion grows when we start talking capacity. In particular the capacity of our electrical charge containers, more commonly known as a **battery**. Given what I stated above you’d think that we’d measure battery capacity in coulombs: how many electrons does it take. Unfortunately, historically we have used **ampere hours**. One ampere hour (**Ah**) is a current of 1 ampere during 1 hour (3600 seconds). Since 1 ampere is 1 coulomb per second, 1 Ah is 3600 coulombs.

Likewise the total amount of power used over a number of hours defines how much must be recharged, or bought from an electricity company. Historically this is measured in (kilo)watthours. 1.2 kWh = 1200 Wh = 1200 watts for an hour. If this power had to be supplied by a typical 12 V battery bank this would be (V * A = W, therefore A = W / V, therefore Ah = Wh / V) 1200/12 = 100 Ah.

**Typical Errors**

Taking one article from a Dutch magazine “Zeilen“, let’s discuss what they do wrong. The article “Geen beweging, toch stroom” (No movement, still current) in the May 2010 issue discusses fuel cells, and shows a few typical examples.

The first small error is a sentence where the author discusses a *Gas generator … with a capacity between 1.5 and 2.2 kWh …* Now kWh is the amount of power delivered over a particular amount of time. Generators are sized in terms of power, e.g. (kilo)watts — not kilo watt hours.

Then he goes on to discuss the admittedly confusing (but correct) wording used by EFOY fuel cells. EFOY rates their equipment by the amount of watt hours they can deliver per day (24 hours). Admittedly, this would be better expressed in simple Watts. The author writes this as follows: *There are five models from 600 to 2200 Watt/h per day, a rather strange and misleading denomination. You should divide the number by 24 to arrive at the true performance. For an EFOY 2200 this coumes down to a maximum current of 7.5 Ah at 12 volt.* Ouch: it should be Watt hour, not Watt per hour (Watt/h). It should also be 7.5 A (amps) not 7.5 Ah (amp hours).

Anyway, on to the next section where he claims that the Protonex M-250C fuel cell delivers *250 Watt per hour*. Guess he means 250 Watt…

And the last one: *The Italian company Acta delivers fuel cells with a capacity of 100, 200 or 1000 Watt during eight hours.* Again, Watts per hour is meaningless.

Guess it’s no wonder that many boaters are confused about electricity with magazines feeding them mis-information like this.

**NOTE:** The above page has been crossposted from my old blog at URL http://yachtelectronics.blogspot.nl/2010/05/basics-of-electrical-units-and.html