Electronics Part 1: Ohm's Law

Today I am starting a series on electronics which will likely go through the whole month. We are going to start with the basics, this week we are learning about Ohm's Law and how it works and how to make calculations based on it. Ohm's Law is the absolute most basic thing there is in electronics. Next week we will learn to apply Ohm's Law to modeling and learn about calculating LEDs and resistors. During this series, we will also discuss turnout motors, signals, switch logic, and basic DCC wiring.

Before we get into Ohm's Law, we need to define four types of measurements. These four terms will be used constantly, and it is important that you know what each one is.

Voltage, measured in volts (E), can be compared with water pressure in a pipe. It is not a measure of how much electricity there is, but the "pressure" behind it. In most model railroading applications, the voltage is 12 volts. However, some light bulbs and LEDs use much lower voltages, which we will discuss later.

Current, measured in amperes or amps (I), is a measure of how much electricity a circuit uses. One light bulb takes a certain amount of current to operate correctly. Two light bulbs use twice as much current. Again, we will discuss in more detail this later.

Resistance, measured in ohms (Ω or R), measures how much the circuit fights back. The circuit components are always trying to block the flow of electricity, and resistance is the measurement of the blocking. However, this is useful. Using a resistor, we can bring down the voltage to light an LED. There are more applications as well, which we will discuss later.

Power, measured in watts (W), is actually a measure of energy, not specifically electricity. Power is not actually defined in Ohm's Law, but it is another measurement that we will use. Unlike voltage and current, which can be changed, power is a direct measurement of how much energy a circuit uses based on what is on the circuit. Energy cannot be created or destroyed, only transformed.

Ohm's Law can be defined as "The current in a circuit is directly proportional to the applied voltage and inversely proportional to the circuit's resistance." So what does that mean? Well, let's break it down a bit: the law defines three things, the current, the voltage, and the resistance, and how they are related to each other. "directly proportional" indicates multiplication, and "inversely proportional" indicates division. Let's make a few equations based of this law:

E=IxR

I=E/R

R=E/I

We can also define how power is related to these other measurements:

P=ExI

Let's take a 60 watt light bulb and figure out what the resistance is and how much current it draws. We know two of the numbers, so let's start with that. We know the voltage is 120 volts and the power is 60 watts. By rearranging the P=ExI formula to solve for I, we get I=P/E. We know P and E, so let's divide 60/120. This gives us a current of 0.5 amps. Now that we know both voltage and current, we can find the resistance. By dividing voltage by current, or 120/0.5, we get a resistance of 240 ohms. There, just like that, we figured out a simple light bulb.

However, most circuits are a little more complicated than that. There is a good trick to remembering those formulas:

So what do these circles mean? Easy. The top half divides with one of the ones on the bottom to find the other one on the bottom. The bottom two multiply together to find the top one. So if you are looking for current (I) and know voltage (E) and resistance (R), the first circle tells you to divide voltage by resistance to find current. If you want voltage, multiply current and resistance together. If you want resistance, divide voltage by current. The second circle works the same way, and is used when you know or want to know the power. The formulas can be hard to remember, but the circles are easy. Just draw the circles on the top of your paper before solving the circuit.

Speaking of solving circuits, let's get started with that. Let's use another light bulb, how about a 100 watt bulb this time. This animation will walk you through the steps:

Simple enough, right? Wrong. That's just the basics. There are also series circuits, parallel circuits, and there's even circuits with both. Series and parallel circuits introduce some new rules in the math. Let's start with a series circuit.

In a series circuit, you have more than one device on the same line. That way, the electricity only has one path to get back to the power source: through both devices. Because of this, the voltage gets split between the two devices, and the current passes through both. So to solve a series circuit, here is how the measurements of the different devices interact with each other:

Voltage is additive. If one device uses 60 volts and the other uses 20 volts, the total voltage will be 80 volts.

Current stays the same. If the total current is 5 amps, it will be 5 amps at each device.

Resistance is additive, just like the voltage.

Power is additive, just like resistance and voltage.

Let's take a look at a strand of Christmas lights. You know, those annoying things that manage to tangle themselves every year? We all spend countless hours trying to figure out which one bulb is dead, because that one bulb shuts off the whole strand. This is because these bulbs are wired in series. There is only one path for the current to follow, and if one bulb is dead, the path is broken, or open. All the bulbs have to be working for the circuit to function, or close. Most of the math is the same as before, so rather than doing a whole diagram again, let's do a more simple problem.

Most Christmas light bulbs operate in 2.5 volts. We wire them in series because we plug them into a 120 volt wall outlet. Because voltage is additive in a series circuit, having enough of these 2.5 volt bulbs strung together in series will add up to 120 volts and we can safely plug the strand into a 120 volt source. So how many of these light bulbs have to be in series to go on a 120 volt source? Let's figure it out. This is a simple problem, all we really have to do is divide 120 by 2.5. That gives us 48. So in order to safely operate 2.5 volt light bulbs on a 120 volt source, you must have 48 of them in series with each other to use up the voltage. Current, however, works differently. There is only one path for the current to take, through each light bulb, so the same electricity in the first bulb lights up all 48 bulbs on the strand. In a series circuit, current stays the same everywhere on the circuit. Assuming a resistance of 8 ohms per bulb, which is a normal value for these bulbs, and multiplying that by 48 (remember resistance is also additive in a series circuit), we get 384 ohms. Now that we are talking about total resistance, we must divide the total voltage of 120 volts by 384 ohms to get our current of about 0.3 amps. Each bulb on the strand uses 0.3 amps, and the total usage of the whole strand is also 0.3 amps. Multiplying this by the voltage tells us that the whole strand uses a mere 37.5 watts.

Series circuits are easy. But we don't use them a lot. Parallel circuits are used more. This is when two or more devices are wired together so that there is a separate current path for each one. That way, when one goes out, the rest can stay lit. However, there is a new set of rules for this type of circuit, which is a little more complicated.

Voltage stays the same in a parallel circuit. If the source voltage is 120 volts, the voltage across each device will also be 120 volts.

Current is additive. If one device draws 3 amps and another device draws 5 amps, the total current will be 8 amps.

Power is also additive.

Resistance is where it gets complicated. Resistance can be calculated by the following formula:

Rt=(R1 x R2)/(R1+R2)

where Rt is total resistance, R1 refers to one resistor, and R2 refers to another. To simplify things a little, if all resistor values are the same, you can simply take the value of the resistors and divide that number by the total number of resistors in the circuit to get total resistance. You might be thinking, this doesn't make sense, the total resistance is lower than each resistor! Well, that's true. As more paths are created, it is easier for the electricity to get back to the source, and so the total resistance of the entire circuit is lower than any path individually. Remember also that current is inversely proportional to the resistance, so as the resistance goes down, current goes up, meaning the circuit uses more electricity with more available paths, which is normal.

Let's take a look at an easy parallel circuit. Again, I won't draw a diagram. We will look at more complicated circuits next week, and I will use diagrams then. But for today, let's do an easy one. Let's take two 100 watt light bulbs and put them in parallel with each other on a 120 volt source, and figure out what the total resistance and total power consumption will be. You can get around the hard math by using the total power (100w plus 100w is a total of 200w) and the source (total) voltage, but let's do it the hard way by using the resistance values of the bulbs. We know that the voltage at each bulb is 120 volts because it is a parallel circuit. We also know the power consumption at each bulb is 100 watts. If we divide 100 watts by 120 volts, we get about 0.83 amps at each bulb. Current is additive in a parallel circuit, so we now know that the total current is about 1.67 amps. The resistance of each bulb can be found by dividing voltage by current, or 120 divided by 0.83, which gives us about 144.58 ohms. Both light bulbs are the same, so both resistance values are the same, so we can simply take the resistance value and divide it by the number of bulbs, or 144.58 over 2, to get a total resistance of 72.29 ohms. We've already figured out our total current one way, but now that we have new numbers, let's check our math by dividing 120 volts by 72.29 ohms. This gives us a current value 1.66 amps, close enough when you consider that we rounded our decimal values during the problem.

Clear as mud? Well, that's all for this week. If you're confused, reread this a few times or make up some practice problems if you want. Next week we will cover more complicated circuits and apply what we learned this week to some common model railroading problems. I hope I haven't made you give up on electronics completely!