Resistance and the Ohm

Resistance is a measure of the opposition that a circuit offers to the flow of electric current. You can compare it to the diameter of a hose. In fact, for metal wire, this is an excellent analogy: smalldiameter wire has high resistance (a lot of opposition to current), and large-diameter wire has low resistance (not much opposition to current). The type of metal makes a difference too. For example, steel wire has higher resistance for a given diameter than copper wire.

The standard unit of resistance is the ohm. This is sometimes symbolized by the uppercase Greek letter omega (Ω). You’ll sometimes hear about kilohms (symbolized k or kΩ), where 1 kΩ = 1000 Ω, or about megohms (symbolized M or MΩ), where 1 MΩ = 1000 kΩ = 1,000,000 Ω.

Electric wire is sometimes rated for resistivity. The standard unit for this purpose is the ohm per foot (ohm/ft or Ω/ft) or the ohm per meter (ohm/m or Ω/m). You might also come across the unit ohm per kilometer (ohm/km or Ω/km). Table 1 shows the resistivity for various common sizes of solid copper wire at room temperature, as a function of the wire size as defined by a scheme known as the American Wire Gauge (AWG).



Table 1. Approximate resistivity at room temperature for solid copper wire as a function of the wire size in American Wire Gauge (AWG).

When 1 V is placed across 1 Ω of resistance, assuming that the power supply can deliver an unlimited number of charge carriers, there is a current of 1 A. If the resistance is doubled to 2 Ω, the current decreases to 0.5 A. If the resistance is cut by a factor of 5 to 0.2 Ω, the current increases by the same factor, to 5 A. The current flow, for a constant voltage, is said to be inversely proportional to the resistance. Figure 1 is a graph that shows various currents, through various resistances, given a constant voltage of 1 V across the whole resistance.


Fig. 1 Current as a function of resistance through an electric device for a constant voltage of 1 V.

Resistance has another property. If there is a current flowing through a resistive material, there
is always a potential difference across the resistive component (called a resistor). This is shown in Fig. 2. In general, this voltage is directly proportional to the current through the resistor. This behavior of resistors is useful in the design of electronic circuits, as you will learn later.

Electrical circuits always have some resistance. There is no such thing as a perfect conductor.
When some metals are chilled to temperatures near absolute zero, they lose practically all of their resistance,but they never become absolutely perfect, resistance-free conductors. This phenomenon, about which you might have heard, is called superconductivity.



Fig. 2 Whenever current passes through a component having resistance, a voltage exists across that component.

Just as there is no such thing as a perfectly resistance-free substance, there isn’t a truly infinite resistance, either. Even air conducts to some extent, although the effect is usually so small that it can be ignored. In some electronic applications, materials are selected on the basis of how “nearly infinite” their resistance is.

In electronics, the resistance of a component often varies, depending on the conditions under which it is operated. A transistor, for example, might have high resistance some of the time, and low resistance at other times. High/low resistance variations can be made to take place thousands, millions, or billions of times each second. In this way, oscillators, amplifiers, and digital devices function in radio receivers and transmitters, telephone networks, digital computers, and satellite links (to name just a few applications).

Current Flow

If a conducting or semiconducting path is provided between two poles having a potential difference, charge carriers flow in an attempt to equalize the charge between the poles. This flow of current continues as long as the path is provided, and as long as there is a charge difference between the poles.

Sometimes the charge difference is equalized after a short while. This is the case, for example, when you touch a radiator after shuffling around on the carpet while wearing hard-soled shoes. It is also true in a lightning stroke. In these instances, the charge is equalized in a fraction of a second. In other cases, the charge takes longer to be used up. This happens if you short-circuit a dry cell. Within a few minutes, the cell “runs out of juice” if you put a wire between the positive and negative terminals. If you put a bulb across the cell, say with a flashlight, it takes an hour or two for the charge difference to drop to zero.

In household electric circuits, the charge difference is never equalized, unless there’s a power
failure. Of course, if you short-circuit an outlet (don’t!), the fuse or breaker will blow or trip, and the charge difference will immediately drop to zero. But if you put a 100-watt bulb at the outlet, the charge difference will be maintained as the current flows. The power plant can keep a potential difference across a lot of light bulbs indefinitely.



Figure 2 Relative current as a function of relative voltage for low, medium, and high resistances.

Have you heard that it is current, not voltage, that kills? This is a literal truth, but it plays on semantics. It’s like saying “It’s the heat, not the fire, that burns you.” Naturally! But there can only be a deadly current if there is enough voltage to drive it through your body. You don’t have to worry when handling flashlight cells, but you’d better be extremely careful around household utility circuits. A voltage of 1.2 to 1.7 V can’t normally pump a dangerous current through you, but a voltage of 117 V almost always can.

In an electric circuit that always conducts equally well, the current is directly proportional to
the applied voltage. If you double the voltage, you double the current. If the voltage is cut in half,
the current is cut in half too. Figure 2 shows this relationship as a graph in general terms. It assumes that the power supply can provide the necessary number of charge carriers.