9.3 Resistivity and resistance  (Page 4/10)

The unit of resistance is the ohm, $\text{Ω}$ . For a given voltage, the higher the resistance, the lower the current.

Resistors

A common component in electronic circuits is the resistor. The resistor can be used to reduce current flow or provide a voltage drop. [link] shows the symbols used for a resistor in schematic diagrams of a circuit. Two commonly used standards for circuit diagrams are provided by the American National Standard Institute (ANSI, pronounced “AN-see”) and the International Electrotechnical Commission (IEC). Both systems are commonly used. We use the ANSI standard in this text for its visual recognition, but we note that for larger, more complex circuits, the IEC standard may have a cleaner presentation, making it easier to read.

Material and shape dependence of resistance

A resistor can be modeled as a cylinder with a cross-sectional area A and a length L , made of a material with a resistivity $\rho$ ( [link] ). The resistance of the resistor is $R=\rho \frac{L}{A}$ .

The most common material used to make a resistor is carbon. A carbon track is wrapped around a ceramic core, and two copper leads are attached. A second type of resistor is the metal film resistor, which also has a ceramic core. The track is made from a metal oxide material, which has semiconductive properties similar to carbon. Again, copper leads are inserted into the ends of the resistor. The resistor is then painted and marked for identification. A resistor has four colored bands, as shown in [link] .

Resistances range over many orders of magnitude. Some ceramic insulators, such as those used to support power lines, have resistances of ${10}^{12}\text{Ω}$ or more. A dry person may have a hand-to-foot resistance of ${10}^5\text{Ω}$ , whereas the resistance of the human heart is about ${10}^3\text{Ω}$ . A meter-long piece of large-diameter copper wire may have a resistance of ${10}^{\mathrm{-5}}\text{Ω}$ , and superconductors have no resistance at all at low temperatures. As we have seen, resistance is related to the shape of an object and the material of which it is composed.

The resistance of an object also depends on temperature, since $R_0$ is directly proportional to $\rho .$ For a cylinder, we know $R=\rho \frac{L}{A}$ , so if L and A do not change greatly with temperature, R has the same temperature dependence as $\rho .$ (Examination of the coefficients of linear expansion shows them to be about two orders of magnitude less than typical temperature coefficients of resistivity, so the effect of temperature on L and A is about two orders of magnitude less than on $\rho .)$ Thus,