In last month’s newsletter, I discussed the physics behind the units of charge (coulombs), Electromotive Force (voltage), current (amperes), power (watts), and energy (joules). To define power and energy, I conjured up the notion of resistance without spending much time on a definition, other than to say it is the property of a material which impedes the flow of electrical current. This month, I will not attempt to expand on this "definition," very much, but, instead, will concentrate on how this ill-defined quantity called resistance is related to voltage and current. This relationship is called Ohm’s Law.

I will discuss why a material exhibits resistance in a future column. To travel there we will have to imagine ourselves as being exceedingly small so we can enter the world of atomic lattices, crystalline structures, and the like. Today, let’s concern ourselves with more practical matters. As in last month’s column, let’s start out using a bit of intuition to develop some qualitative concepts, i.e. "common sense." Building on the common sense concepts, we will progress to a more quantitative level and develop some formulas which you may find useful.

Consider the simple circuit depicted in Figure 1. It consists of a variable voltage source, a variable resistance and two conductors (wires). Assume the voltage is set to some constant arbitrary value, V, that does not vary with time (direct current). Also, assume the variable resistor is set to an arbitrary value, R. Remembering last month’s discussion of Electromotive Force, you will see the voltage source will cause a difference of potential to exist between points A and B, the two ends of the resistor. Since the resistor creates a path between points A and B, a current, I, will flow through the resistor. This current will be constant since the voltage source is continually replacing the charges at point A which are flowing from point A to point B, through the resistor. Thus, the voltage source can be likened to a pump, in many respects. As long as the arbitrary settings of V and R remain the same, a constant current I will flow through the resistor. Since this circuit forms a single loop, the value of current, I, flowing through the resistor has to be the same as the current flowing elsewhere around the circuit. In other words, at any point around the circuit, a current of value I is flowing. Another name for this type circuit is a "series" circuit.

So, we have our little circuit with current, I ,chasing ‘round and ‘round. But, what happens if we increase the voltage to a new setting? Using your intuition, a bit of reflection will lead you to the conclusion that increasing the voltage will increase the current to a new higher value. What about lowering the voltage? Using the same logic, the current will decrease. More voltage means more current; less voltage means less current. Another way of saying this is the current is directly proportional to the voltage.

Returning to Figure 1, again, for a moment, what happens if the voltage setting is left constant and the variable resistance is increased? Let’s see, a resistor impedes current flow, so setting ours to a higher value should result in less current flowing. Likewise leaving the voltage constant and reducing our resistance should result in an increased current flow. More resistance: less current; less resistance: more current. Another way of saying this is the current and the resistance are inversely proportional.

These are just the kinds of experiments one Mr. Georg Simon Ohm was conducting for real in the early 1800’s. Mr. Ohm, a German who lived from 1787 to 1854, tested every kind of material he could get his hands on and empirically developed the relationships between voltage, resistance, and current we have just discovered intuitively. Mr. Ohm’s research led him to the formula I=V/R. Stated another way: current is directly proportional to voltage and indirectly proportional to resistance. Sound familiar? To prove this to yourself, make up some numbers for V and R and determine a value for I. Now, use the same number for R, but make V a larger number. Is I smaller or larger? You should find it is larger. Now keep V the same and make R larger. I became a smaller number, right? Congratulations, you have just reverified Ohm’s Law.

Now, back to Mr. Ohm’s formula for a moment. The formula I=V/R says if you know V and R, you can determine I. What if you don’t know V, but you know I and R? Or maybe you know R and I, but want to know V? Well, you mathematicians out there know where I am headed. Other forms of Ohms law are:

V=IxR, and R=V/I.

A handy little tool, the "magic circle," shown in Figure 2, can help you remember these relationships. Cover the quantity you want to know with your fingertip, and the tool will tell you which of other two quantities you need to multiply or divide. Try it, you’ll like it! Oh, one more thing I must tell you since you have just gotten your arms around Ohm’s Law. Mr. Ohm discovered another thing during all his testing. Not all materials conform to Ohm’s Law. How’s that again??!! It turns out there are "Ohmic" materials, and "Non-Ohmic" materials. In "Ohmic" materials, resistance is independent of changes in voltage and current. In "Non-Ohmic" materials, resistance is dependent on V and I and does not vary linearly. Isn’t that just like physics? Just when you get a handle on something, something else comes along and blows the theory all to pieces. Not to worry, however. Most materials you will come across in practical electronics are of the "Ohmic" variety and Ohm’s law hold up just fine!

Well, that’s it for this month. Have fun with Mr. Ohm’s discovery!

For further reading on this subject, try:

1) ELECTRONIC COMMUNICATION, by Robert L. Shrader, ISBN 0-07-057150-3

2) Any High School of College Physics Textbook. I have PHYSICS, by Paul A. Tipler, ISBN 0-87901-041-X

3) ARRL HANDBOOK FOR RADIO AMATEURS, ISBN 0-87259-173-5