Wednesday, July 16, 2008

IMPEDANCE SERIES PART 7, Lee week 8

July 16, 2008 Educational Radio Net, PSRG 8th session

Much like any radio talk show I will "set up" the topic and then allow time at the end for questions or comments. In reality most fundamental ideas in electronics and radio are best described mathematically but, given that we do not have a "white" board for graphic illustration, I will attempt to convey fundamental ideas verbally.

This session is the 7th in the impedance series. Given that impedance is the combination of reactance and resistance and, further, that reactance is an alternating current phenomenon it is clear that we must have some elemental definitions under our belts to fully appreciate the subject. This multi-part narrative series is an attempt to elevate participants to an intuitive level of electrical understanding without using any serious mathematics as well as provide some review for those of us who have not spent a lot of time on fundamentals lately.

Where are we going with these discussions? Once we have the notions of electrical current, voltage, and power well in hand I will introduce the physical property of materials called resistance and then merge the voltage, current, and resistance trio into the workhorse notion of Ohm's Law. Subsequent parts of the series will introduce DC, or direct current, AC, or alternating current, and followed by capacitance and inductance, then reactance, and, finally, I will introduce impedance as the combination of resistance and reactance. All discussion material will be reviewed continually and be available on the blog.

Part 1 developed the idea of electrical current consisting of moving charge and defined the ampere as 1 coulomb of charge moving past a fixed point in 1 second. One coulomb was defined as a collection of charge numbering 6.24 x 10^18 electrons.

Part 2 developed the notion of mechanical "work" and considered objects at different "potential" levels in a gravitational field. The concept of "voltage", also known as electrical potential difference, and the relationship of voltage to current follows closely with the idea of a mechanical weight being moved between different levels. In both cases work is being done and energy is being manipulated in various ways.

Part 3 capitalized on Bob's lightning series to review electrical current in the context of a charged cloud redistributing charge in the form of lightning where modest amounts of charge make a large impression if moved rapidly.

Part 4 developed the notion of potential difference and ended with a definition of voltage. If you move 1 coulomb of charge from point A to point B in an electric field such that 1 joule of work is done then the potential difference between points A and B is defined as 1 volt. Another way to state this is that 1 joule of energy is required to push 1 coulomb through a potential difference of 1 volt.

Part 5 developed the notion of power by using a mechanical analogy. Power is the relationship between energy and time. Specifically power is the change in energy, known as delta P, divided by the change in time, known as delta t. Conversely, energy is power multiplied by time.

Part 6 developed the notion of resistance by using a simple circuit to compare how well various materials conduct electrical current. We looked at a simple series circuit with fixed voltage, one D cell battery, a fuse, an ammeter, a switch, and a pair of DUT terminals. Substituting various materials across the DUT terminals yielded different measurements on the ammeter and we ranked these materials based upon their "conductance". Finally, we learned that resistance and conductance are reciprocals and that high conductance equals low resistance and vice versa.

Part 7, tonight's edition, will deal with the relationship of voltage, current, and resistance in the context of Ohm's Law. We will use the same series circuit as last week but substitute a variable voltage supply for the fixed D battery and also include a voltmeter across the DUT terminals.

But first let's talk about a very interesting question which arose during last week's session.

Someone asked how one would count a coulomb of charge consisting of 6.24x10^18 electrons. Glen, K7GLE, offered an electrochemistry definition of the coulomb and, after due consideration, I think that it will be instructive to talk a little more about how a physical chemist might go about measuring a coulomb of charge using nothing more than a sensitive laboratory balance.

Let's start by thinking about a carbon atom. Looking at a periodic table one finds the atomic weight of carbon to be 12. Now, by definition, the gram molecular weight of carbon is 12 grams and is called a mole of carbon. Checking the periodic table again for silver we find the molecular weight to be 107.87 so one gram molecular weight of silver is 107.87 grams and is called a mole of silver. The interesting point is that both a mole of carbon and a mole of silver contain the same number of atoms. Early researchers worked long and hard to determine how many constituent "things" were in a mole and the number turned out to be approximately 6.022 x 10^23. So, bottom line, a mole always contains the same number of atoms and this number is known as Avagadro's number. I used carbon as the comparison element but, in fact, carbon is the defining element for this number.

Now, let's talk about electroplating with silver. Atomic (or metallic) silver is neutral but if atomic silver loses one electron then it becomes ionic silver and has a charge of +1. Ionic silver is very soluble in water whereas atomic silver is not. Imagine that we have a good, strong, solution of ionic silver and that we insert a couple of electrodes into our silver solution. If we connect a battery to the electrodes then one electrode will be positive (known as the anode) and the other negative (known as the cathode). Now, given that our silver ion has a positive charge of 1, the silver ion will be attracted to the negative cathode which has an abundance of electrons. When the silver ion touches the cathode then an electron is handed to the silver ion and it changes to metallic silver and is plated out on the cathode. As long as the battery is connected to the electrodes and until the solution is exhausted the silver ions plate out on the cathode. Clearly, as time progresses, the cathode will become heavier as more and more silver is transferred from solution to cathode.

If Avagadro's number of electrons, 6.022 x 10^23, were added to the ionic silver then we would plate out 107.87 grams of silver on the cathode. Remember that one ion of silver plus one electron produces one atom of metallic silver. However we are only interested in a coulomb of electrons so, given that there are fewer electrons in a coulomb than "objects" in Avagadro's number we will plate out less metallic silver. In fact, one needs about 96,506 coulombs of charge to equal Avagadro's number. So, dividing 107.87 grams by 96505 gives us the weight of silver per coulomb. The final number is 1.12 mg of metallic silver for every coulomb of charge added to the ionic solution.

So, a bit of cleverness plus a sensitive balance will change the problem from the difficult counting of individual electrons to a much easier weighing of a cathodic electrode.

Note also that if 1.12 mg of silver were deposited every second then we could conclude that the battery plating current is one ampere as in one coulomb per second.

Any questions or comments on this alternate method of measuring charge?

Ok, on with Ohm's Law which deals with the relationship of voltage, current, and resistance.

Let's modify last week's series circuit with which we looked at resistance by changing the D battery to a variable voltage DC power supply and adding a voltmeter across the DUT or "device under test" terminals. Still a simple series circuit but now we have some control over circuit voltage and we can now measure voltage. So, from power supply positive we go to a fuse, then a switch, then an ammeter, then DUT terminals and back to the power supply negative terminal. Finally we add the voltmeter to the DUT terminals.

Now, after poking through a drawer of parts, we find a carbon resistor with the value 1000 ohms marked on it. If you are able to read the color code it would be brown, black, red.

Let's attach this one k-ohm resistor to the DUT terminals, set the supply voltage to 10 volts DC, and flip the switch to on. The ammeter moves upscale to 0.01 amperes or 10 milliamperes. Now double the voltage to 20 volts and the ammeter reads 0.02 amperes or 20 milliamperes. Halving the initial voltage to 5 volts causes the ammeter to drop to 0.005 amperes or 5 milliamperes. Regardless of what values you assign to the supply voltage or DUT resistance you will find that the circuit current is directly proportional to the voltage and inversely proportional to the circuit resistance. In other words higher voltage across a given resistance yields higher current and higher resistance with the same voltage yields less circuit current. This is a straight line curve if plotted and the effect is said to be linear.

The bottom line is this... current is voltage divided by resistance. Double the voltage and double the current... double the resistance and halve the current. That is Ohm's Law in a nutshell.

This concludes the set up discussion of Ohm's Law. Are there any questions or comments?