## Wednesday, July 23, 2008

### IMPEDANCE SERIES PART 8, Lee week 9

July 23, 2008 Educational Radio Net, PSRG 9th session

This session is the 8th 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 belt 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? So far we have talked about electrical current, voltage, power, resistance, and 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.

Let's review what has been covered up to this point in the series.

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 as in work done divided by the change in time to do the work. 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 as in Device Under Test. 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, developed the notion of Ohm's Law by using a simple series circuit to illustrate the relationship of voltage, current, and resistance. Ohm's Law states that electrical current through a resistive device is directly proportional to the voltage across the device so, for example, doubling the voltage across the device will double the current through the device. This relationship stated in math terms is I (which is the symbol for current) equals E (the symbol for voltage) divided by R (the symbol for resistance).

Part 8, tonight's edition, will contrast direct current and alternating current.

Ok, on with direct current and alternating current.

To illustrate the difference between DC and AC think of a clear vinyl tube about 1 foot long and which is filled with sand. About half way down the tube we scribe a "line" across the tube perpendicular to the long axis of the tube. So, we can look at the tube and see the relationship of sand to the scribed line. Assume that particles of sand represent electrons which are free to move if influenced by some motive force such as voltage.

Let's attach a source of voltage, or motive force, across the tube ends by using a battery. Watching the scribed line we notice that the electrons as represented by the sand particles always move slowly to the right (or left if the battery were reversed) with respect to the line. Given that sand represents electrons, or current, this constant motion represents direct current or DC. We know that the number of sand grains in the vicinity of the scribed line is huge. Suppose that we identify 6.24 x 10^18 grains of sand and call the assemblage a coulomb of sand. If our coulomb of sand moves past the scribed line in exactly one second then we can say that one ampere of sand is moving in the tube. Note that the current does not "zip" down the tube quickly from end to end rather the sand "drifts" down the tube and we get our ampere because lots of sand is drifting past the scribed line every second. As long as motive force, in this case a fixed voltage, is applied to the tube ends the sand, or current, continues to move in one direction.

Suppose that we have a second scribed sand tube identical to the first. Suppose further that we have no idea what is connected to the ends of the tube. Looking at the scribed line we notice that sand is drifting to the right, stopping, then reversing its motion to the left, then stopping, then reversing motion to the right. Back and forth with respect to the scribed line in a very regular manner. By carefully counting grains of sand we notice that a coulomb of sand moves to the right past the scribed line in one second then reverses and moves to the left of the line in the next second. We are watching an ampere of alternating sand if you please. Remember from the DC example above that reversing the battery caused the sand to reverse direction. Watching the sand reverse direction regularly suggests that the voltage at the tube ends is reversing regularly as well. Since the sand represents electrical current we are watching alternating current or AC. The sand motion is caused by the motive force at the tube ends so alternating current or AC is caused by an alternating motive force or alternating voltage.

Simple enough but there is a gray area here. Direct current sand may speed up, slow down, or stop completely but the direction never changes. Suppose that the sand mostly goes to the right but on occasion stops and moves a bit to the left then continues on to the right. This would be an example of superimposed AC and DC. If the AC component peak is less than the DC value then the mix of the two will look like unidirectional DC. True AC is generally considered to be periodic and could be produced by a square wave voltage or a sine wave shaped voltage which is symmetric about the zero voltage axis.

If a circuit contains only resistance then Ohm's Law works equally well for both AC and DC. The R for resistance and the Z for impedance are interchangeable. The entire point of this series is to show that impedance is resistance combined with reactance. Reactance is an AC phenomenon hence goes away in the steady state DC world rendering resistance and impedance identically the same.

Next week we will talk about the heating effects of AC vs DC and talk about equivalent waveforms including how various values are calculated.

This concludes the set up discussion of AC vs DC. Are there any questions or comments?
This is N7KC for the Wednesday night Educational Radio Net.