# Electrical Quantities B

#### Basic Electronics and Units of Measure

During our last period of instruction, we discussed among other things voltage, current and resistance and we pick it up now with the discussion about Ohm's law.

### Ohm's Law

Ohm's law is a very important electronic principle that ties together these three items of voltage, current and resistance. George Simon Ohm expressed the relationship between current, voltage and resistance in ... A long time ago, 1927 and this principle bears his name. What does Ohm's law say? Well, it states this that current the current that flows in a circuit is directly proportional to the voltage across the circuit and is inversely proportional to the resistance in the circuit.

It is expressed mathematically like this so it's I = V/R or and it's actually a little more common to see it written like this that the V is expressed as E. As we go through this course if I write it as E, which is my more common way of doing it, it means the same thing as V. I = E/R so what's this say? The current that flows in a circuit is directly proportional to the voltage. If R were to stay the same and I were to increase then E would increase as well. We're going to forget about this one for a moment, if voltage remained the same and resistance were to increase then I would decrease and likewise if resistance went down current would go up. We're going to look at a few examples to make this a little bit more clear.

### Current is Proportional to Voltage

The first one we're going to look at is that current is proportional to voltage. What we have here is three meters that are setup and we have a battery here. This is a voltage and this is a resistor and we have the same scenario setup in all three. What we're saying here, is that the higher you apply voltage to a circuit the greater the current will be.

In this scenario we're looking at this particular formula I=E/R that is current equals voltage divided by resistance. In this case, we have a 10V battery, a 20V battery, and a 5V battery. We're going to say that this resistance is going to stay the same. We'll say that this is going to be a 10-ohm resistor all the way across. Using Ohm's law, we would come in here and we'd say well the voltage is 10 and the resistance is 10 so given that the current equals 1. Here we have our meter and our meter for our purpose is we're going to say is indicating one amp of current. Then we come to our next one here and here we have 20V and resistance is 10 and now the current has gone up to two amps.

Now remember the part of Ohm's law that we're looking at is this part, that says that voltage is directly proportional to current and so you'll see a direct proportion here. We have 10 with one amp of current. When we double the voltage the current also doubles. In this case here with the same voltage applied and in this case resistance drops to … Excuse me the voltage drops to five volts and the resistance is 10 so now the current drops in half and you notice the meter here is going down. In all cases, voltage is directly proportional to current.

If we were to graph this, let's see, if we had our voltages were what 5, 10, 15 and 20 and our currents were what, 0.5? Let's see we had 1 and 1.5 and 2 something like that and in our first scenario we had applied 10V across 10 ohms and we had one amp of current that right there. The next one we applied 20V with and we had two amps of current right there and then we reduced the voltage on the last one and we had five volts and about ½ amp of a current right there. If we were to graph this we would see that it is linear as voltage increases, current increases and vice versa.

### Current Versus Resistance

Now, the second part of Ohm's law said current is inversely proportional to resistance. The rule here is that as current goes up resistance goes downs and as current goes down resistance goes up. Let's take a look at this one. In this case, we're going to be looking at a stable voltage. The voltage is going to remain 100 and we'll say 100 here and 100 here and we're going to vary the … We'll start out with 20 ohms and then we will increase the resistance to 40 ohms. Then we are going to decrease it down to 10 and we're going to look at what happens in this particular circuit.

Here, we start out with 100 with 20 ohms and that will give us 5 amps of current. Then we're going to leave the voltage the same and we're going to increase the current. Now, according to Ohm's law they're inversely proportional so the resistance was 20 it goes up to 40 so now there should be a decrease in current and we do the math here and we get about 2.5. Resistance went up, current went down and here we're going to drop the resistance dramatically what was it? One hundred we're going to drop down the resistance to 10 ohms and now the current jumps quite a bit. Okay.

Okay, again in this relationship and remember these are the meters indicating the values, this was our starting point indicating this scale we increased the resistance, current went down. Here we decreased the resistance and the current went up.

### Current Versus Resistance Inversely Proportional

If we were going to look at this on a graph let's see we started out with what was our initial voltage? We started out with 100V and 20 ohms of resistance. In this particular case, we started out with 20 ohms of resistance and remember our current was 5 amps. Then we increased our current to or our resistance to 40 ohms and that decreased our resistance to about 2½. Then we decreased our resistance to 10 ohms let's see on our scale that would be about right here and our current was at 10 amps. You see here we have an inversely proportional relationship between current and resistance we no longer have a linear curve as we did with voltage and current.

Another important thing we might note from this is that a part of Ohm's law was this formula right here that E= IxR. In this particular scenario we had, 100V as the applied voltage throughout we just changed the resistance and if you will note here IxR here 10x10 is 100 and 20x5 is 100 and 40x2½ is 100 so this relationship of IxR is also part of Ohm's law.

### Alternate Forms of Ohm's Law

These are the three formulas we just talked about. It is imperative that you commit these three formulas to memory and that when you look at surface you're able to like visually in your head just apply these formulas and get rough ideas of what voltage is and current should be. These are not optional formulas in the field of electronics these are a must-know and they are really the foundation of calculations for electronics circulatory.

### Electrical Power

The next one is electrical power and we're going to … Electrical power is a measure of the rate at which energy is used and it's measured in watts. Electrical power is dissipated as heat. Based on Ohm's law, power calculations are determined with this formula here P=IxV or you could say also IxE, either way.

At any rate, current times voltage gives us power in what we call watts and when you get an electric bill, ultimately what you're paying for is the power that you have consumed and it is measured in watts. Now other variations of this formula look like I2R and if we were to, let's see if we could derive this from this particular formula if we say IxV, which is this formula right here, something that's we'll notice is remember from Ohm's law voltage is equivalent to what? Remember voltage is the same thing as IxR isn't it? If we replace IxR with V and then we have our I over here we can simplify this equation to say, I2xR and so that is the same thing as this.

Vice versa, we can go over here and again if we have IxV and this formula right here, we can derive this formula. Now what you might recall is current. Current is a function of … In Ohm's law it is the same thing as voltage divided by resistance. If we replace I with VxRxV, we can derive the equation V2/R. Again this is an equivalent way of calculating power so you can use this formula, this formula or this and these three are stated right here.

Here we have a simple circuit. What is the power dissipated by the resistor and the circuit below? Let's see if I can bring out my handy dandy little formula. Let's see, here we have remember to calculate current, remember we divided voltage by resistance so if we said 100 divided by and this the 10k resistor. If we said 10 zero exponent three and equals we would have a current of 10 milliamps. According to our formula, P=VxI times current. We have 10 milliamps if we take that current times and we apply voltage times 100 we would get 1 watt.

Likewise, we had our other two formulas. We said I2R, we said I2xR or V2/R. If we brought back our little formula or our little calculator here, let's see. If we said, we had a current of 10 exponents minus three that was 10 milliamps. We said I2xR, so if we square this times our resistance which is 10 exponent three, it should equal one again. Then we could do the other formula here, let's clear our calculator and if we said 1002 and we will divide that by the resistant, which is 10 exponent three, we should again get one so we have 1 Watt of power dissipated by this and we have looked at three different ways of calculating power for this particular circuit.

### Conductance

Next item we are going to look at is a subject called conductance. Conductance is the inverse of resistance. It expresses how literally current can flow through a material. The unit of measure for conductance is G. It's referred to as Siemens (S). At one time, the unit of measure was called Mhos, (that is Ohm's spelled backwards) because it's the inverse of ohms. Relationship between resistance and conductance is expressed by, and you will know G=1/R. Whatever resistance is 1/R will be the conductance and is measured in Siemens. The pictured resistor has a resistance of 10,000 ohms. Its conductance would be 1/10,000 or 0.001 Siemens.

### Electrical Quantites, Abbreviations, Units, and Symbols

Here we have some electrical quantities and abbreviations and we've got two pages of these and we haven't covered all of these subjects. In fact, I'm going to briefly jumps to the other one here. I do want to mention them; I'm not going to go into all of them at this time I want to give you a sense of what we are looking at though. Because, throughout the course of this book we will be looking at all of these items.

For example, Capacitance, the symbol for Capacitance is C, the unit of measure for Capacitance id the Farad and the abbreviation for Farad is F. If you are looking at electrical schematics, you might see C3; this would be indicating probably a specific capacitor and the value of that capacitor would be 0.002 Farads. Likewise, Conductance the symbol is G, Siemens the abbreviation for Siemens is S and G5 would indicate a device that has the 0.01 Siemens would be the value of conductance for that component. Here we have frequency, which is measured in hertz, and like I said, I'm not going to go over all these at this point. The F here means frequency and the 60hrtz is the actual valley of frequency in Hertz.

Let's jump over to the next page. Power we talked about power, watts, power here would be referring to a specific problem probably and the power is 150 watts. Resistances, the value of resistance R 140 Ohms voltage. The form just might be refereeing to a test point equals 12V.

Okay, in this lesson, we have looked here at the electrical quantities, abbreviations, units and symbols. We took a look at the value of conductance and we found the conductance was whatever the value of resistance is; the conductance was effectively the reciprocal. We also looked at electrical power and we tried three different ways of calculating the power for this specific circuit. We got the same results with all three formulas and these were the three formulas we used P=IxV, P=I2xR and P=V2/R.

We also looked at the forms of the Ohm's law and you will need to commit these to memory. We looked at the part of Ohm's law that says that current is inversely proportional to resistance and we graphed that and we measured it on a situation where we had a voltage that remained the same where the changing resistance. We saw as the resistance went down, current responded in an inverse manner.

Then we looked at the first part of Ohm's law that says that current is proportional to voltage and we hooked up a current meter to a battery and a resistor, we left the resistor at one value, we changed the voltage and we saw that the current changed in a proportional manner. Then we looked at what is Ohm's law, we discussed I=V/R or I =E/R.