Resistance, Resistors and Ohm’s Law

What is resistance? The most common definition of resistance is the opposition to current flow—more specifically the flow of electric charge in a material. The circuit element used to model this behavior is the two terminal resistor. Resistors are measured in ohms and represented by the symbol R. The circuit symbols for the various type resistors are shown in Figure 1.

Conceptually, we can understand resistance if we think about the moving electrons that make up electric current interacting with and being resisted by the atomic structure of the material through which they are moving. In the course of these interactions, some amount of electric energy is converted to thermal energy and dissipated in the form of heat. This effect may be undesirable. However, many useful electronic devices take advantage of resistance heating such as irons and hair dryers.

Most materials exhibit measurable resistance to current. The amount of resistance depends on the material. Metals such as copper and aluminum have small values of resistance, making them good choices for wiring used to conduct electric current. In fact, when represented in a circuit diagram, copper or aluminum wiring isn’t usually modeled as a resistor; the resistance of the wire is so small compared to other elements in the circuit that we can neglect the wiring resistance to simplify the diagram.

For purposes of circuit analysis, we must reference the current in the resistor to the terminal voltage. We can do so in two ways: in the direction of the voltage drop across the resistor or in the direction of the voltage rise across the resistor. If we choose the former, the relationship between the voltage and current is

v=i*R\;\;\;\;\;\;\;\;\;\;\:(1)

where v = the voltage in volts i = the current in amperes R = the resistance in ohms.

If we choose the second method, we must write

v=-i*R\;\;\;\;\;\;\;\;\;(2)

where v, i and R are as before, measured in volts, amperes and ohms respectively. The algebraic signs used in equations (1) and (2) are a direct consequence of the passive sign convention.

The above equations are known as Ohm’s Law after Georg Simon Ohm, a German physicist who established its validity early in the nineteenth century. Ohm’s low is the algebraic relationship between voltage and current for a resistor. In SI units, resistance is measured in ohms. The Greek letter omega (\Omega) is the standard symbol for an ohm.