May 14, 2011

EE Fundamentals: Ohm's Law

After a few conversations with more than 50% of my viewership, I have decided that maybe I got ahead of myself with some of these electronics topics. To bring things down a bit I am going to start introducing very simple, short discussions about the fundamental tools for looking at electronics. These EE Fundamentals segments will discuss the building blocks any hobbyist will need when getting into electronics. One of my goals in starting this blog was to open up the world of hobby electronics to anyone who may have a passing interest, but over these last few months I have, admittedly, gotten away from that idea. I will still be addressing more advanced topics and my personal projects in between these building block segments. 

The logical place to start this off is with the law that everyone has probably heard of and most likely forgotten in the years since high school physics: Ohm’s Law. Back in the early 1800’s, Georg Ohm published his observations regarding the relationship of voltage and current. In his experiments he applied various voltages to different lengths of wire and measured the resulting current to determine their dependence on one another. His observations became known as “Ohm’s Law”, where the current through a conductor is directly related to the voltage applied by the equation:

V (voltage) = I (current) * R (resistance)

For a visual demonstration, Figure 1 shows a linear relationship between voltage and current across and through a 1 ohm resistor. You can see in the graph that at each voltage along the x-axis there is a current of the same magnitude. Ohm’s law holds for this device as, in this example, 3 volts = 3 amps * 1 ohm. 

 Figure 1. Voltage and Current relationship in a 1 ohm load resistor

But what is the best way to visualize this concept without just looking at a graph? To answer that you must first understand the general natural of the three terms involved: voltage, current, and resistance.

Voltage:            Think of voltage, measured in volts, as an electrical pressure or force. When you apply a voltage to a conductor (say, for instance, a copper wire) you are actually pushing charges through the wire, causing them to flow away from the source of the applied pressure. The way I think if it is by picturing a garden hose. When you push down on the nozzle, the pressure built up inside the hose causes water to flow outward.

Current:            Current, measured in amps, is the result of a voltage difference across a conductor. The key to current flow is to have one end of the conductor at a lower potential than the other end of the conductor. If, for instance, you applied 5V to the end of a wire and 5V to the opposite end of the wire, the net current flow would be zero because there is no potential difference to draw the charges. Just as heat transfer occurs when one area is warmer than another, current flow occurs when one side of a conductor is at a lower potential than another.

                          Humans often perceive current as the flow of electrons from a positive voltage to a lower voltage or “ground” at 0 volts. This is inaccurate in a few different ways. First, the word “current” is commonly associated with the flow of electrons. However, if you noticed in my description of voltage I used the term “charge” rather than electrons to describe current flow. The reason for this distinction is because the flow of current depends on the material you are working with and the voltage applied. In some cases, positive charges (called holes) make up the bulk of what is perceived as current flow. I would like to go into the details on this one but semiconductor physics may be a bit much at this point.

                          The second thing worth noting about current flow is that we analyze circuits based on the “conventional current” model, where charge flows from positive to negative. Essentially, this means we are modeling charge flow in terms of positive charges rather than electrons, but in most cases they are still referred to as electrons. It turns out this is of little consequence as long as the polarities of all voltages and currents are kept consistent when analyzing the circuits. As Figure 2 shows, we can model current flow from the positive lead of the 5 volt source to ground (at 0 volts) as long as we consider the voltage drop across the 100 ohm resistor as positive.

Figure 2. Current flow in a simple circuit

Resistance:      Electrical resistance, measured in ohms, is physical property of a material characterized by its ability to resist the flow of current. Everything everywhere has electrical resistance to some degree. Some materials have very low resistance to the passage of current (conductors) and others have a very high resistance (insulators). Again, the resistance of a specific material comes down to physics that I don’t want to touch on in these posts. However, resistance is highly dependent on a few key factors: length of the conductor, the cross-sectional area, and the temperature of operation.

Now let’s re-examine Ohm’s law with this improved understanding. Ohm’s law states that the amount of pressure you must apply to a conductor to get a desired charge flow is equal to that charge flow multiplied by how much the conductor will try and oppose it. Therefore, if a material doesn’t want to let current pass through it, you really have to push hard to get it to cooperate (resulting in high voltages). The same argument applies for passing large amounts of current through a material with very little resistance. Figures 3 and 4 show how to create the same current flow under two different voltage/resistance combinations. In Figure 3, a 5 volt source and a 100 ohm resistor produce a current of 50 milliamps. In Figure 4, the voltage has increased by a factor of 10. To get the same current as Figure 3, the resistance must increase by the same factor according to Ohm’s law.

Figure 3. 50 milliamps of current generated with a 5V DC source

 Figure 4. 50 milliamps of current generated with a 50V DC source

We call components that adhere to Ohm’s law “ohmic” and those that do not “non-ohmic” (clever I know). Resistors are ohmic because an increase in voltage across the resistor creates a linear escalation in the current flowing through it. Examples of non-ohmic components include capacitors, inductors, sausages (unconfirmed), and diodes.

So that is Ohm’s Law in a nutshell….at least using DC power. AC (alternating-current) Ohm’s law is basically the same idea but slightly more complex (pun intended for anyone who gets it). This went a little longer than I was shooting for but having a solid understanding of the fundamentals makes more complex ideas easier to digest.


Noah Ryan said...

Awesome! The analogy of having to push current through a resistor is really helpful. I never thought of resistance as a scaling factor for converting voltage into amperage before.
I'm still a little hazy on the meaning of current though.
in the diagram
| |
| |
_ |
- |
_ |
- |
| |
C |

Where the A, B, and C label locations in the circuit (and the ~~~ is the resistor), is there a difference between the current at any of the labels? If the -5 at one end of the power source is added to the +5 at the other end we get the required 0 result (right?) and the extra 0 has no effect. The 0 is different from the +5 and the -5, so does this difference draw both positive "holes" and negative electrons from the ends of the power source? And, in general, what foodstuffs *are* ohmic and which are not?
I'm so confused.

Noah Ryan said...

Arg! The spacing was lost in my beautiful ascii art diagram! And it won't accept the pre tag! Well, my question still stands, and the parts of the circuit I was asking about are just the wires connecting the components.

Chris said...

I have no idea how to read the diagram so I am going to answer your first question with 42.

As for your second question, I think the only the only way to adequately catalog ohmic and non-ohmic foods is to test.....for science....

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