Electric Resistance and Resistivity

Figure 121.

Resistances can range from extremely small numbers of ohms to very large numbers of ohms. Ceramic insulators have 1012 ohms, while copper wires have resistances of 10-5 ohms. Superconductors are nonohmic because they do not have any resistance at all. Resistance is related to the shape of an object and what it is made of.

The phrase IR drop refers to the voltage drop across a resistor. If voltage drops across a resistor, this is referred to as the IR drop, which is similar to the drop in fluid pressure that occurs when a pipe has resistance to flow. There is going to be conservation of energy so that, when a resistor has an IR drop, the energy will be dissipated as heat energy. The voltage applies energy that is dissipated as heat. The energy supplied by the voltage source and the energy converted by the resistor will be equal. The IR drop will equal the voltage output in a simple circuit.

ELECTRIC RESISTANCE AND RESISTIVITY

The resistance of an object, as mentioned, depends on the material it is made of and its shape. In a simple cylinder, the resistance is proportional to its length, similar to that of flowing water through a pipe. The resistance, too, will be inversely proportional to the cross-sectional area A of the cylinder. The equation is that the resistance is equal to the resistivity multiplied by the length and divided by the area. Figure 122 is the relationships seen in a cylinder that has resistance:

Figure 122.

The resistivity is an intrinsic property of the material, independent of the shape or size of the object. Objects can be conductors, semiconductors, and insulators, based on their degree of resistivity. Most resistors will have fixed atoms that don’t allow the flow of electrons. Semiconductors have an in-between status, which makes them important in modern electronics.

Resistance varies by temperature. Some superconductors will have zero resistivity at low temperatures. Resistivity increases with increasing temperature in the case of conductors. This is because atoms will have more collisions at higher temperature so that resistivity will be higher. Over a small increment of temperature, there is a temperature coefficient of resistivity, which helps define the difference in resistance with temperature.

Certain alloys will have limited temperature dependence and will have a low temperature coefficient of resistivity. This coefficient will be high and positive when the resistance is temperature dependent and increases with temperature. There may be a negative coefficient of friction, in which the resistance decreases with temperature. This is true of semiconductors. Semiconductors will be more conductive at higher temperatures (and will have low resistivity) because there will be freer electrons at a higher temperature. The coefficient of resistance will not be linear and consistent over greater ranges of temperature.