When electric current flows through a metal wire or through other circuit elements, it encounters a certain amount of resistance, the magnitude of which depends on the electrical properties of the material. Resistance to the flow of current may be undesired, for example, in the case of lead wires and connection cable or it may be exploited in an electrical circuit in a useful way. Nevertheless, practically all circuit elements exhibit some resistance; as a consequence, current flowing through an element will cause energy to be dissipated in the form of heat. An ideal resistor is a device that exhibits linear resistance properties according to Ohm’s law, which states that
V = IR Ohm’s law
that is, that the voltage across an element is directly proportional to the current flow through it. R is the value of the resistance in units of ohms (Ω), where
1 Ω = 1 V/A
The resistance of a material depends on a property called resistivity, denoted by the symbol ρ; the inverse of resistivity is called conductivity and is denoted by the symbol σ. For a cylindrical resistance element (shown in Figure 1), the resistance is proportional to the length of the sample, l, and inversely proportional to its cross-sectional area, A, and conductivity, σ.
Fig.1 The resistance element
It is often convenient to define the conductance of a circuit element as the inverse of its resistance. The symbol used to denote the conductance of an element is G, where
Thus, Ohm’s law can be restated in terms of conductance as:
I = GV
Ohm’s law is a realistic relationship that finds widespread application in electrical engineering, because of its simplicity. It is, however, only an approximation of the physics of electrically conducting materials. Typically, the linear relationship between voltage and current in electrical conductors does not apply at very high voltages and currents. Further, not all electrically conducting materials exhibit linear behavior even for small voltages and currents. It is usually true, however, that for some range of voltages and currents, most elements display a linear i-v characteristic. Figure 2 illustrates how the linear resistance concept may apply to elements with nonlinear i-v characteristics, by graphically defining the linear portion of the i-v characteristic of two common electrical devices:
The typical construction and the circuit symbol of the resistor are shown in Figure 1. Resistors made of cylindrical sections of carbon (with resistivity ρ = 3.5×10−5 “-m) are very common and are commercially available in a wide range of values for several power ratings.