Ohm’s Law and What It Can Tell Us

allel section of the circuit will be quite close to the voltage at the beginning of the circuit. It’s not too hard to see that by using series-parallel circuits, manufacturers can save a lot of money on switches, wire, and circuit protectors, but series-parallel circuits also greatly simplify a boat’s overall electrical system, with no sacrifice in performance or safety.

Circuit Protector

Battery Switch “On”

Switch “On” Switch “On” Switch “On”

Cabin Light Cabin Light Cabin Light

Fig. 1-5. A series-parallel circuit as found on your boat.

Georg Simon Ohm (1787–1854), a German physicist, was one of the great early experimenters with electricity. He left us with the simple but oh-so-important mathematical formula that bears his name. Ohm’s law helps us to understand the relationship between the measurable forces in electricity. Once we are armed with a clear understanding of the relationships between the different elements in this formula, we will have made a giant step forward in our ability to understand and locate electrical problems.

As we work with this invisible thing called electricity, we need to get used to dealing in an abstract way with the stuff. We’ll be taking a lot of measurements with a multimeter, and we will learn to translate these measurements into meaningful information. Throughout the rest of this book I demonstrate the correct methods of obtaining accurate electrical measurements with a multimeter, and I try to provide an understanding of what these measurements mean. First, however, we must get the definitions of a few electrical terms clear in our heads, and then become completely familiar with this wonderful thing called Ohm’s law.

The Key Players

Therearefourtermsthatwillcontinuallycropupin anydiscussionofthingselectrical: volts,amps,ohms, and watts. Eachofthesetermsrepresentsanelectrical valueandisnamedafteranearlyexperimenterin electricity.Thesearethepeoplewhocapturedthe conceptofelectricityandmadeitusefultopeoplelike youandmewhoownboats.Thereisafifthterm,also namedafteranearlyexperimenter,that’sgaining favorwiththeknowledgeableandtrendyamongus, the joule.

The unit of electrical resistance, the ohm, was named for Georg Ohm, the German scientist who gave us Ohm’s law. The electrical symbol used to express the value for ohms is the Greek letter omega, shown in figure 1-6 on page 6.When used in Ohm’s law, however, resistance is represented by a capital R.

Alessandro Volta (1745–1827) was an Italian physicist who gave us the unit of electrical force called the volt. The electrical symbol for volts is so simple that it doesn’t need an illustration; it’s just a capital V. However, when used in the formula for Ohm’s law, voltage is represented by a capital P, which stands for potential.

Andre-Marie Ampere (1775–1836) was a French physicist whose namesake is the electrical unit that describes the rate of electrical flow through a circuit that we call the amp. The electrical symbol for amps is a capital A. When working with Ohm’s law, we use a capital Ifor amps. James Watt (1736–1819) was a Scots mathematician credited with significant improvements of steam engines who coined the word “horsepower” to measure the amount of work a machine is doing. Horsepower is fine for measuring large amounts of energy, but it doesn’t work for the small amounts that we have to measure while working with electricity, so, in honor of this ancient Scot, we call the electrical unit of power a watt and use a capital Eto represent it. Watts aren’t used in the formula for Ohm’s law, but they are important in a corollary to Ohm’s law, called the pie formula (because P × I = E, as we will soon see), that we will be using to calculate the size of wires and circuit protection.

James Joule (1818–1889) was an English chemist credited with the discovery that heat is a form of energy. Thus, a joule is a unit of electrical energy equal to the amount of work done (or heat generated) by a current of 1 amp acting for 1 second against a resistance of 1 ohm. The symbol for a joule is a Jand it also is not used in Ohm’s law calculations. Joules aren’t really important for the work that we do throughout the rest of this book. I wouldn’t even mention them here if it weren’t for the fact that the joule is gradually replacing the watt in some areas of electricity (joule is also replacing calorie in the list of nutritional information on many food packages) and that you’ll probably run into it in your other reading. When you do hear the term, you’re fairly safe in assuming that 1 joule = 1 watt.

So you can see that our foundations of electricity are named after quite an interesting international rogues’ gallery of electrical scientists.

Let’s forget about joules for now and take a look at each of these other terms more closely, and perhaps we can begin to get a clearer picture of their importance to us. Fi 16Fig. 1-6. The ohm symbol, the Greek omega.

Voltage

Voltage is the measure of the potential that an electrical power source has for doing work for us. Thus, a fully charged 12-volt battery has the potential of producing 12 volts (actually closer to 13.5 volts) of power. In fact, the term electrical potential is often used instead of the word voltage and means the same thing. To refer back to the analogy of the water tank, where a hose connected to the bottom of a tank might measure 100 pounds per square inch (psi) of water pressure, a wire connected to a 12-volt battery (in a circuit, of course) will measure 13.5 volts of electrical potential. In both cases we are referring to the energy that’s available to do work and nothing else; the voltage in the battery is exactly the same concept as the water pressure in the tank. Simply think of voltage as electrical pressure. The higher the voltage in the battery (or in any other source of electrical power), the more pressure is available to send electricity along its path in a circuit.

Amperage

Amperage is often confused with voltage, and I think it’s the most difficult of all our definitions to grasp. Think of amperage as the rate of electrical flow past a given point in a circuit. If you can think of voltage as electrical pressure, then it should be easy to think of amps as the volume of electrical energy flowing through a point in a circuit. Amperage is most important in my mind because too much of it in a circuit is what trips circuit breakers, blows fuses, melts wires and other components, and sometimes burns up boats. This stuff needs to be carefully controlled, and much of the rest of this book will be devoted to understanding how to do just that.

Resistance

Resistance, as we said, is measured in ohms and is that invisible force that holds back electrical flow (amperage) and reduces the electrical potential (voltage) as electrical energy flows through a circuit. It’s also the electrical unit that puts electricity to work for us. For

example, it’s the resistance in the element of a light bulb or the toaster in your kitchen that makes the element glow and give off light or toast your bread. And it is the rapidly fluctuating resistance in microscopic transistors (measured in tiny fractions of an ohm) that makes the wonderful world of marine electronics possible. In marine wiring, unwanted or excessive resistance is caused by such things as loose or corroded connections, wire that is too small in diameter, or wire runs that are too long.

One noticeable by-product of resistance to electrical flow is heat. In the case of the toaster, we have engineered a way to make this heat useful. In the case of a loose or corroded connection, the heat generated is sure to cause damage to the area around the connection; read melted switches and plug connections. Figure 1-7illustrates Mr. Ohm’s formula.

Ohm’s Law

No, you don’t have to worry about going to jail for breaking Ohm’s law. In fact, you can’t break it (not without a nuclear particle accelerator that costs many millions of dollars), because it is, for all practical purposes, inviolate—you couldn’t break it if you tried. Simply stated, Ohm’s law is a mathematical formula we can use to calculate any one of the values we mention above as long as we know the value of any two of the first three. For example, if we know the amperage and resistance for a circuit, we can easily calculate the voltage, or if we know the voltage and amperage, Ohm’s law gives us the resistance. Once we know the amperage and the voltage, we can calculate the wattage using a simple little formula, called the pie formula, that we will get to in a moment (“Working with the Numbers”).

It’s important to note here that various versions of the following formulas exist, assigning different letter designations to the elements of the formula (Efor volts or sometimes watts, for example; the letter Iis often used to designate amperage as well). The point is that it really doesn’t matter what letter you use, as long as you know which value it’s assigned to. For our purposes we’ll keep it simple and use Vfor volts, Afor amps, Wfor watts, and Rfor resistance or ohms. Figure 1-8on page 8 shows the simple equation used to find watts, or amps if voltage and wattage are given.

Ohm’s law works out rather nicely for us as boaters because we will always be able to measure at least two of the values we need to calculate the third. Voltage (V) and amperage (A) are both easily measured using a basic multimeter, and we will learn how to do this later. With some circuits, ohms (R) are a little tricky to measure accurately, but we’ll learn how to handle them also. For our purposes, wattage (W) is not measured but calculated from voltage and amperage, or information often provided by the appliance manufacturer.

Fig. 1-7. The Ohm’s law equation. This circle provides a visual relationship between the key electrical players. If any two of the values are known, the third can be found by using either multiplication or division. By multiplying amps times ohms, voltage can be found. By dividing voltage by ohms, amperage can be found. Dividing volts by amps determines resistance (ohms). Notice that if voltage remains constant and if resistance increases, reduce amperage flow and vice versa. This explains mathematically why a short circuit to ground, before power reaches a load (resistance), is so dangerous. Amperage will go way up until either a fuse blows or a breaker trips, or something burns up! Conversely, it also explains why, if resistance increases (loose connections, too small a wire), amperage needed by the appliance won’t be delivered.