## Wednesday, July 2, 2008

### IMPEDANCE SERIES PART 5, Lee week 6

July 2, 2008 Educational Radio Net, PSRG 6th 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 5th 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 you might ask? 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 AC, or alternating current, and DC, or direct current, 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, tonight’s edition, will deal with the notion of power.

Ok, on with the idea of power.
Let’s first look at the mechanical side of the picture. Imagine a water tower and let’s say that it is 100 feet tall. There are two ways on this particular tower to get from the ground to the top. The first way is via a ladder from ground straight up the side of the tower to the top. The second way is via a spiral ladder from ground to the top of the tower. Let’s further say that the straight ladder has 100 rungs, or steps, from bottom to top and the spiral ladder has 300 steps from bottom to top. Now imagine identical twins and that both weigh exactly the same. One twin decides to use the vertical ladder to climb the tower and the other prefers the easier route so chooses the spiral staircase. Let’s say that both move along the respective ladders at 1 step per second. The twin traveling up the vertical ladder reaches the top in 100 seconds and the twin on the spiral ladder reaches the top in 300 seconds. Now the question arises… which twin performed the most work going from ground to tower top? Well, given that the twins weigh identically the same and that both traveled the same 100 feet vertically, the answer is that they did identical work to achieve the tower top. Since it took the vertical traveling twin 100 seconds to climb to the tower top and the spiral twin took 300 seconds to achieve the top it is clear that the spiral twin took 3 times longer to make his trip. From this we can conclude that the vertical twin performed the same work as the spiral twin in 1/3 the time so his power output was 3 times that of the spiral twin. The bottom line is that power is a measure of how quickly work is done.

Remember that work and energy are identically the same and that both are measured in units called "joules". So, regardless of whether we are dealing with mechanical or electrical phenomenon, power is the change of energy over time as in joules per second. The unit of power is the watt and one watt is defined as 1 joule per second. In DC, or direct current related phenomenon, electrical "power" is simply electrical current in amperes times potential difference in volts. If comparing a 100 watt transmitter to a 300 watt transmitter you can say that the more powerful 300 watt unit moves 3 times more energy to the antenna than the lesser power unit in the same amount of time. More energy in a given time translates to a stronger radiated field.

Power is power period. Audiophiles will be familiar with the term RMS power as in root mean squared power. There is no such thing in the physical world as RMS power. This is a cooked up term used by audio amplifier manufactures to rate their products. You can plot power as a function of time and then calculate the RMS value of the waveform but the number calculated has no relationship to anything in the real world. We have not talked about AC or alternating current and alternating voltage at this point but let me assert that, in the AC world, power is the product of RMS voltage and RMS current. Power is power is power. Simply the measure of energy changing with time.

Now, let’s consider the kilowatt-hour meter on the side of your house. If power is energy divided by time then it follows from algebra that energy is power times time. So the Kw-H or kilowatt-hour meter measures how much electrical energy you use in your home. At this point in time residential home owners only pay for total energy consumed in the home. Industrial meters also measure what is called "demand" or how fast energy is delivered hence "power" as well as total energy used.

This concludes the set up discussion of power, both electrical and mechanical.. Are there any questions related to the concept of power?

This is N7KC for the Wednesday night Educational Radio Net.